We did a nice tour of the Cyclades last year - Syros, Tinos, Mykonos, Naxos, Paros, Ios, Folegandros and Santorini
Of that lot the only one we wouldn't go back to is Santorini, behind the stunning facade its a shithole, expensive one at that. Mykonos is mega expensive but had an amazing time there.
But I'd say the best of them was Folegandros and Paros.
My Advice is get a flight to Athens and then pick up the ferries from Pireaus.
You can island hop in the true sense if you don't go in high season, but if you're in high season book your hotels with Booking.com or similar and work your way around the islands.
Better to pick a group of islands like the cyclades and just explore - a few days on each island.
Only issue is that you have to plan the logistics around ferries, but its dead easy to do and ferries are cheap