You need to let us know which month, but I'd also suggest perusing the previous forum posts--lots of good Greek honeymoon trip info here.

I...want it to be on a quiet secluded island with nice beaches, lots of history, great restaurants, not a lot of tourists either.

Wouldn't we all? I'm afraid any island with all those attributes will attract lots of tourists, except during off-season, of course. Your best bet of finding something close to what you are looking for is to pick an island with no airport or cruise ship harbour. Another would be a quiet resort on a very large island like Crete. "Quiet and secluded" could include islands like Amorgos,

It's in June, Heimdall.

June is a great month for the Greek Islands, as weather has settled but high season not yet begun. The islands with the most to offer are also the most popular, so you are going to have to compromise in one way or another.

Santorini is a popular honeymoon island, with recently reopened Akrotiiri, the Minoan site, but also has lots of cruise ship visitors. Mykonos is another touristy island, not so busy in June, and has Delos, the archaeological site, on a nearby island.

For less touristy you could go to Naxos or Paros, both of which have day trips to Mykonos and Santorini from the middle of June. These islands both have sandy beaches, good restaurants, and some nightlife. Slightly more out of the way would be Amorgos or Folegandros, both with good hiking and spectacular views.

You don't have to limit yourself to the Cyclades. There are several other island groups in Greece, and none are more than an hour from Athens by air. You might think about Skopelos in the Sporades, location of the film "Mamma Mia". The Cyclades are easiest to reach from Athens by ferry, one reason why they are so popular.

Ok, I checked out Santorini and it seems beautiful.

Hello bkluvsNola and congrats!

Santorini is quite possibly the most "touristised" island of Greece. For a reason of course, but you have to decide if you really want to go somewhere without many tourists and what this means, or go on the very beatten track and compromise.
As you mentioned beaches, note that Santorini is favored for its unique landscape on the caldera (cliff) side. Beaches are located on the other (flat) side of the island and consist of black volcanic rock/pebbles/grit that many people dislike.

I was about to mention a few options outside Cyclades, but you need to specify what you want and offer some ideas to help you narrow the, down. Right now I see you are all over the place : ) What about reading a couple of guidebooks or having a look on greeka.com and greek-islands.us ?

MYKONOS, and you can take a ferry to Delos.
Awesome trip, we did that for our honeymoon, then took our daughter back there 10 years later.

mariha:

Requirements:
* great views
* island with decent beaches, sand preferred
* opportunities for snorkeling perhaps?
* interesting short hikes
* great food/restaurants
* reasonably priced hotels
* not too many tourists or too crowded

Many of those things are subjective but here are a couple of ideas:

LEMNOS - North-East Aegean
* great views -Not sure what this means especially as sea side level provides mostly water views, but I have enjoyed some great sunsets from Platy beach on Lemnos. On some clear days you may about make out Mt Athos at the very distance. On the east side of the island you may see Turkey on the distance.
* island with decent beaches, sand preferred -Lemnos has many varied beaches, many of them sandy, as Platy or Thanos
* opportunities for snorkeling perhaps? - Snorkelling+ sandy beaches do not team up. Usually there is more life on rocky surroundings. That said Lemnos have some rocky/pebbly beac hes too such as Kaspakas.
* interesting short hikes Again not sure what interesting hike is, but you may walk along some beaches or among a few inland villages on Lemnos.
* great food/restaurants - Island is not so extremely known so less visitors so more less need to import products from other areas. There are some great local wines, lots of local fish offered on taverns and unpretentious Greek food all over.
* reasonably priced hotels- This can mean anything to different people but I think Lemnos is good value for money and a similar hotel on popular islands such as Cyclades may cost double Lemnos rates. A few larg-ish resort hotels and then mostly appartments, small B&Bs, rooms to let on Lemnos.
* not too many tourists or too crowded- I mention Lemnos as exactly a hugely undiscovered island. Some Australians and New Zealanders of Greek origin or coming from families whose granpas fought on WW2 battles, visit every now and then. There is one or two hotels aimed to UK visitors. But quite possiby North Americans have never heard of it and it is mostly Greek visitors around. Most action is around its main port town, Myrina, then there are many other very quiet villages around. June is a quiet month on Lemnos, so quiet that you may prefer visit towards the end of the month that early June.

LEFKAS- Ionian Sea

* great views - Very scenic towns and landscape, more green than other islands. The side facing mainland (Nydri, Lygia etc) offers interesting views of mainland and various islets. Lefkas Town is pleasant too. The other side offers some of the most photographed beaches in Greece. There is an interesting interior too with mountain villages.
* island with decent beaches, sand preferred - The calm side of the island towards mainland offers mostly averrage pebbly/sigle beaches. The other side offers great sandy beaches but there are more currents in the sea and often wind. Popular for windsurfers, might or might not suit you for everyone. You may want to google Kathisma, Egremni,Porto Katsiki, Agios Nikitas to see what I mean.
* opportunities for snorkeling perhaps? - Vasiliki or Lygia might fit the bill, see previous comments on snorkelling. There are many excursion boats from Lefkas taking in surrounding islands and islets. Many of them do swim stops and you may enjou snorkelling too. If you are willig to hire a car, note that LEfkas is connected to mainland only on a small floating bridge. So you may go off exploring parts of mainland too. There are many interesting towns, beaches and rocky coves there to enjoy.
* interesting short hikes - There are some, the one from Nydri up to Dimosari waterfall been the most popular, other hikes among/around mountain villages mostly available too.
* great food/restaurants - Lefkas is famous in Greece for some of its local products such as pasteli and madolato sweets, ladopita and other pastries, its soumada ( a local almod liquer) and of course its wines. I find restaurants good value for money especially if you are willing to spend a visit up on the inland villages. Even on touristy places such as Nydri, there are some great restaurants, for example I find Pines restaurant one of the best value for money I met all over Greece.
* reasonably priced hotels - Lefkas is a great value for money, this is why it gets more and more popular among Greeks and other nationalities. Again, you may want to clarify what kind of hotels/budget you are after. Mostly appartments or small hotels, only a couple of upscale hotels on Lefkas, Ionian Blue and Galini (I find Galini more value for money)
* not too many tourists or too crowded - On June Lefkas is not extremely busy. A lot depends on your exact location too. Many people from former Yugoslavia, Bulgaria etc invade the island on August and many Italians and Scandinavians favore Lefkas for its watersports on July/August. June is still a tranmission month, mostly Greeks, some UK visitors and a few of a varied crowd. Lefkas town and Nydri will be the busiest, rest of resorts more quiet. In general not too crowded.

Santorini or Mykonos have their own beauty but have exhausted themselves with tourists.In June you can certainly meet all of your requirements on islands like Paros and Naxos. Plus there are smaller islands you can day trip to from there. Going more remote is not necessary - June is not too crowded on those islands and there is enough activity if you desire a little nightlife.

"Not too many tourists or too crowded" is a time of year, not a location. In July and August any island worth visiting will be crowded, and smaller ones are the worst. In June it is busy enough to get interesting, but not overcrowded anywhere, even on Mykonos and Santorini. Paros and Naxos are fairly quiet in June, a time popular with Scandinavian families whose school holidays start then.

Personally June is my favourite time for the Greek Islands. Many couples prefer September, when children are back in school and the season is winding down. It's also the best time for swimming, with water still warm from the summer.

Where do you live?

Don't hold your hopes up high for snorkeling in The Med. There is more sealife in our local swimming pool, if you have been to the Caribbean etc it will be a huge disappointment.

Look at the Ionion, Cephalonia and Ithaca are beautiful and it easy to island hop. The beaches in this area are however fairly poor. Crete has some good beaches and the snorkeling off the south coast is OK.

While it's true that snorkelling in Greece isn't as interesting as places with coral reefs (found mainly in the tropics) it can still be fun. The best snorkelling will be in small coves where the fish can take shelter rather than on long sandy beaches. I have snorkelled on Australia's Great Barrier Reef, but still bring my snorkel and mask every time I travel to Greece. In the Aegean the water is crystal clear with great visibility. You will see lots of little fish, and even a small octopus if lucky.

BTW, I wouldn't care to swim in Dickie_Gr's local pool!

As Dickie has suggested, Cephalonia (Kafalonia) may fit the bill. On a sudden impulse (Ryan Air special) we spent 4 nights/5 days here. You will want to rent a car. Myrtos beach is one of the most beautiful beaches world-wide.

This is the hotel we stayed at. It is very secluded in a small town; the drive to it is nothing to write home about, but once ensconsed in this lovely walled-in haven with it goregous flowers and trees, interesting rooms and most gracious hosts Caterina and Barry you hardly want to leave it. The food is fantastic and Caterina will cater to your specific culinary interests if you have a hankering for something specific (she fixed seafood paella just for us!) They do have 2 very well behaved pooches, just in case you have allergies, so you don't get surprised.

The island has been destroyed by major earthquakes so it may appear more "rustic" than you are looking for, but the scenery and hiking/swimming is fantastic.
http://www.booking.com/hotel/gr/museum-george-molfetas.en.html

http://www.greeka.com/ionian/kefalonia/kefalonia-beaches.htm

congratulations on your upcoming honeymoon!

Kefalonia has some great beaches, Myrtos has been voted a few times amongst the most beautiful beaches of the world..
But there are other very nice sandy beaches as well...

A would recommend staying in beautiful Fiskardo in the north of the island, there's a great romantic hotel i'd like to recommend : http://www.arthotel.gr/emelisse/

Myrtos is a terrible beach. It looks great on film but It is 50oC in winter due to the white cliffs reflecting the sun. The beach is simple stone and again in any sort of heat it is silly hot to stand on. The sea again suffers from vastly differing temperatures due to the shallows being full of white stone, as a result the sea isn't clear to snorkel in.

Snorkeling in the Med : I spent 38 years doing this 3 times a year. 6 years ago I went to the Caribbean for the first time. I don't pack my mask now on trips to the Med.

I can't think of a more romantic place to laze about than Fiskardo.

Hi Dickie_Gr,

I can understand why the Med may be a letdown after snorkelling somewhere like the GBR, Red Sea, or Caribbean, but not everyone gets to go there. I wouldn't go out of my way to snorkel anywhere in Greece, but a snorkel & mask doesn't take up much room in the suitcase, and gives you something to do when you tire of sunbathing. You don't need to bring swim fins if all you want is a quick paddle around.

And hey, tell your local swimming pool operator to use more chlorine!

I have been on Lemnos,Lefkas,Paros,Naxos on June. Lemnos is the less staightforward, much less tourists around,Lefkas is more straightforward but still not too many visitors on June,Paros and Naxos are very on the beaten track and many visitors around.
(I have been on Cephalonia on June more than 15 years ago too, so I do not think I can comment on this island).
I have in my mind that someone pointing as critiria on where to go "not too many tourists around", means a more secluded holiday, a more quiet destination than others not a more quiet destinations comparing to July and August. It would help to clarify what exactly OP means.
I am very familiar with Naxos and Paros (and many other members here are) and can offer advice, I am just not sure if that is what they are looking for! I like thinking out of the box every now and then too. It doesn not have to be Cyclades Cyclades and Cyclades plus Crete and Rhodes when reffering on Greek Islands!

Ooops, reading my post again I realised it might sound a bit sharp. I was tryting to explain my line of thinking, not critisize other people's suggestions.I hope you do not get me wrong! (Not easy not to be native English speaker sometimes....)

Heimdall

I know and I did see a stingray in Mallorca last year.

The sea life in the Ligurian Sea is world class. I think the Med just suffers the same as everywhere, lots of people generally means less wildlife.

I am aware of a few Great White Sharks prowling around Elba and Sicily, there is a theory that they go there to mate.

Most of the wildlife in our local pool is around seven years old, male and very loud. The chlorine doesn't seem to deter them, maybe they need to use DDT.

"Paros and Naxos are very on the beaten track and many visitors around." Again, this depends upon what you expect and when you go. I have been on Paros in June and it was so quiet we were looking forward to more folks arriving.

One advantage of the Cyclades is they are easy to reach from Athens by ferry. So Paros and Naxos are "on the beaten track", but there are resorts on each island that won't be at all busy in June. On Paros you could look at Aliki or Drios, but both are a little out of the way.

Antiparos is a laid back island island with good beaches and restaurants, but not much in the way of historic sites. It's actually easier to reach from Parikia, the Paros port, than some places on Paros itself. The small settlement to the south of the island, San Georgio, is quiet, has a great beach, and a hotel that would be excellent for a quiet honeymoon: http://www.dolphinantiparos.gr

But we haven't hear back from the OP ? I agree this is up to what you expect and they might come and throw a word on how many touristsd are too many or something?