Fly to Izmir and then ...? Bus service must surely be available. There are low cost flights between Istanbul and Izmir, although it may be too late for the cheapest fares. Check out Onur Air and Pegasus Air.

You can take a bus from Istanbul, it's just a bit of a haul. I did a similar trip but broke it up by taking a bus to Canakkale, staying there for a night to see the ruins of Troy and then took a bus from there to Selcuk (20 minutes from Kusadasi).

You can still get cheap rates.

Try the web sites of Atlas Jet and Onur Air in addition to THY.
Atlas and Onur provide free shuttle to Selcuk.

There is very frequent minibus from Selcuk to Kusadasi for the less than 20 mile trip to Kusadasi for a very small amount.

You will lose too much time on the bus to Kusadasi from Istanbul and will not save much over the flight cost unless you have a lot of luggage.

Bus usually leaves Esenler Otogar and will be quite frequent also. there may be buses from Harem on the Asian side which is easier to get to and faster, but you should check. Try Ulusoy, Metro, Truva, Kamil Koc, etc.

Otogar

It suddenly dawned on me that this is auto gare

Michael, we had an Armenian math teacher in high school who was very fond of saying frequently, "Good morning after supper."
Unfortunately, my dear father used to say it also, and it would always bug me. So, I hope you do not mind my writing it here.

light bulbs are generally turned on in the evening.

thanks everyone, my kids (22 and 25) are doing the traveling and they arrive Feb 7th. Still not sure of anything. So keep the advice coming! Hotels, hostels etc!

Michael said "It suddenly dawned on me that this is auto gare"

LOL, I thought you would have known that, Michael, with all the borrowings from French that Turkish has.

Yeah, you see these signs, assume they're in Turkish and undecipherable. Then you say the word out loud and it's obvious, especially in context. I had the same light bulb about otogar and also about kastana.

kastana ??? I must be dense.

Chestnut? Kestane?

Like castagna in Italian = chestnut. Maybe I'm more familiar with that word than others. When DH and I were first married, we bought, at the import store, this interesting-looking basket for our dirty clothes. When we showed it off, my new father-in-law, an Italian immigrant, fell over himself laughing. It was a chestnut/castagna basket from Italy.

That's what I thought, but my German and even more so my Italian are not strong enough for the switch to go on.