I haven't got any hotel recommendations to make for honeymooners, but do make sure you check the sailings before you do any hotel bookings. It wouldn't be fun to have a super-duper room reserved in Ios if there is no boat on that day (or, worse still, if your friend turns up at the port at 8 in the morning only to find that there was one boat and it left at 05:30).

Actually, seeing as your friend (obviously) likes going by boat, I would probably skip Ios (never been there, but it does have a backpacking reputation), and fly from either Mykonos (preferably, as Aegean fly there) or Syros to Corfu via ATH. Corfu is well worth a couple of days, and from there one can sail to Italy in well-appointed ferries. In fact, ANEK go direct from Corfu to Venice!

Other parts of Italy worth seeing are the SW, e.g. Napoli, Salerno, Capri, Pompei and Sicily...