Transport between the three islands relies on local ferries and these are unsophisticated ‘landing-craft’ style boats that do little more than ferry passengers and vehicles in Spartan comfort, but they are very functional and vital to the inter-island communication. There is plenty of on the ground support excursions and infrastructure and the islands are well-used to tourism; the only exception is that travellers will need to use a bit of independence in getting between the islands.
I think Naxos would be the best island for you: incredible beaches, wonderful villages, great restaurants, and some very good hotels (though I don’t think I’d go so far as to call them hip – but nice, for sure). The farther south you go from Naxos Town the quieter the beaches get – so keep going to find the balance you prefer. If you want an island with a little more hip but beaches not quite as perfect then try Paros. If you want to err on the quieter and idyllic side then Antiparos or Ikaria.
Since St. John is part of the U.S. Virgin Islands, U.S. citizens can visit without a passport. There are quite a few bargains on both St. Thomas and St. John right now, so it’s a good choice for travelers on a budget. Snorkelers should not miss visiting Trunk Bay, one of the best snorkeling spots in all of the Caribbean for seeing amazing marine life.