What other islands beside Santorini and Mykonos do you recommend?

Paros and Naxos are both good, popular choices for a first-time visitor. Milos looks really pretty, although I haven't been there so can't verify. Another one I haven't seen, but would like to, is Folegandros. Both Milos and Folegandros are less touristed than Paros or Naxos. I'd recommend that you do some research. Google all of them, to see what looks most appealing. Check out their hotels on Trip Advisor; the hotel reviews often give you insight on the island itself. Look at Matt Barrett's website, www.greektravel.com/?, and also check out this website: http://www.greek-islands.us/ Have fun planning!

There were easy ferry connections between Crete and Santorini when I visited Greece back in the day. I suspect that they are still good. Crete is very different than the smaller islands, but I really enjoyed it. Pam

Loved Naxos! We were "stranded" there for 3 additional days because of gale force winds preventing ferry travel. Car rental was very reasonable. The locals were wonderful and treated us like family. Our hotel was terrific - on a cliff overlooking the sea. They went out of their way to see about getting us on a ferry back to Athens since my flight was leaving the next day - 11:30 pm they drove us to town to get tickets. Food was great. I'm not much of a beach bum but there was lots to do and see.

Rhodes is colossal!!!!

Go to Crete. Totally different from the other Greek Islands. Ferries run from Santorini to Crete - Heraklion and Ayios Nikolaos. Places to see there - numerous Minoan sites, Knossos being the biggie. The archaeological museum in Heraklion and the beautiful Venetian harbour at Chania (a personal favourite). Cuisine is slightly different from the traditional Greek, hotels tend to be smaller family run. The better beaches are on the south side of the island. Good hiking in the gorges. Atmosphere definitely laid back - long leisurely lunches at small tavernas, excellent local wine and raki (but watch out for the latter, it creeps up on you!). Recommend you have a look at the Rough Guide to Crete for more information.

As others have noted, Naxos and Paros are good options. From Santorini, Folegandros is a smaller more laid back island, if you have 3 or 4 days to devote Crete is good, though for pure relaxation Koufonissia would be my pick.

I enjoyed Paros with a side trip to Antiparos. Antiparos has the oldest commercial cave in the world. Its not the prettiest cave in the world, but interesting for its history.

I would also suggest Paros. (I lived in Greece for a few years, and really enjoyed visits to Paros. I stayed at Silver Rocks Hotel).