Hi annex3,
This is a good plan for your trip in Greece. I would suggest you save Athens for the end so you are there and will avoid any missed connections on your departure day. If you can fly right to Santorini from London, I'd do that to save time. 3 days in Athens will give you a chance to see the Acropolis and Plaka plus a museum or two. 4 days on each island will give you a nice visit. Remember you will lose at least a half day taking the ferry between islands, but you have chosen well - you will have two very different experiences. You do not need to use a travel agent, especially since you are planning well ahead. But it is up to you if you want to spend the time researching places yourself. I often reserve ferry tickets online to get a definite time or specific ferry, but I have also changed or bought tickets there. I would think in June that you would be fine to buy your ferry tickets once you get to Santorini. The regular ferry from Naxos to Piraeus (Athens) will take about 6 hours and a high speed about half that time. I enjoy the regular ferry because you can get outside and watch the passing islands, unlike the high speed. It takes about 2 hours on the ferry from Santorini to Naxos.

I agree with everything parosblue wrote. Fly directly to Santorini if you can, either a non-stop flight from Gatwick with easyJet, or from Heathrow via Athens with Aegean Airlines.

There is no need to prebook either the Santorini-Naxos or the Naxos-Piraeus ferry — just buy your tickets when you get to the islands. Recommend using the Blue Star conventional ferry rather than a highspeed or sea jet. Blue Star offers wonderful views leaving Santorini, and that leg takes only 2½ hours, so you can spend the whole time on the outside deck if you wish. With the Sea Jet you are confined to an inside cabin.

For Naxos-Piraeus you can take the highspeed if you wish, and in this case it will be a large Hellenic Seaways car-carrrying catamaran. Journey times are shorter, and the highspeed leaves Naxos later in the morning. Ironically, though, Blue Star arrives at Piraeus about the same time in the afternoon. I have taken both types of ferry, and prefer Blue Star.

Your plan for three days in Athens and four on each island is good. If you want to see Athens from an Athenian's perspective consider one of the walking tours offered by http://www.athens-walks.com. I have heard good things about this company, especially their unique food tour.

Four days on each island is fine, but depending upon your interests consider three days on Santorini and five on Naxos. That would give you time for a day trip from Naxos to Delos/Mykonos, or to have an extra day on the beaches.

I agree with Heimdall on the island split.
3 days on Santorini is sufficient to chill out and soak up the views while 4 on Naxos gives you more time to tour about or visit the various beaches.

Santorini 3 days, Naxos 5 is better.

Thank you for all of your input. Do you think 2 full days in Athens is enough?

Two full days in Athens is enough to see the major sites, but more would be better. Everyone who has visited Athens multiple times sees something new on every visit. You will be visiting Santorini, but did you know that most of the frescos discovered at the Akrotiri site there are displayed at the National Archaeological Museum in Athens? There are many other examples of Cycladic art displayed in Athens rather than on the islands.

It's your trip, so decide for yourself how much time you want to spend at each destination. I used to return from the islands the same day as my flight home, but began to realize how much I was missing. If you plan to return to Greece again, you can see more of Athens on the next visit.

I would suggest any visitor to Athens spend at least two full days exploring the Acropolis and museum as well as the surrounding Plaka area. The National Archeology Museum is one not to miss as well. Two days will scratch the surface - whether it is enough for you depends upon interests and your vacation expectations. You mentioned that you are traveling with a family of three. Will there be a young child or teen with you?