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.
My fiancee and I are heading to Greece in July. We’ve been to Naxos, Paros, Mykonos, and Santorini. This time we plan on being there July 1 to 23. We’re definitely including Milos, and one of Paros or Naxos. Any recommendations for other islands? Any particular ferry routes we should consider? Some “less touristy” islands are a must (for at least one island). We can be lively or very chilled. Thanks and best wishes!