When you say cruise do you mean yacht cruise or great big, running into raock, type cruising. Certainly yacht cruising in Greek islands is a great idea and tend to be for a week or two weeks.

You might also like to think about Turkey for similar or local wooden boat tours "Gulet" which can be for any number of nights, you can hire the whole thing or go with a mixed (unknown group)

You might also like to look at Croatia and the many islands scattered through the Adriatic

I think you can take a ferry from Bari to Dubrovnik (a lovely fortified city) or Ancona to Split. From either of these ports you can get out to the islands (by mini ferry) or partake in some island hoping yacht work. I spent a week on Brac a couple of years ago and our day out in Split (including the Roman palace) was an eye opener.

Louis Cruises offers cruises to the Greek islands with Piraeus as homeport, so that you could easily combine a cruise with a stay in Athens.
http://www.louiscruises.com

If you wish to visit 1-2 Greek islands, then you don't really need a cruise for that, you can do it on your own.
You could visit islands such as Naxos and Paros, or Mykonos and Tinos that can be reached in a couple of hours from Athens.

Flying into Rome and out of Athens is a very good idea. For the time in-between, you need to decide whether your focus will be shipboard activities (cruise) or islands (travel from Athens by flight or ferry). With a cruise you will spend most of your time aboard ship, with maybe 6-10 hours on each island, while travelling by ferry you will spend only a few hours aboard ship and the rest of the time on an island. Most flights from Athens to the islands take only 30-45 minutes.

Many people love cruises, and there's nothing wrong with that. For me, though, I enjoy the relaxed atmosphere of the islands, never having to look at my watch, and going everywhere at my own pace. You can't do that during port calls on a cruise.

I love to start the day on an island with a leisurely breakfast at a sidewalk cafe, then spend the day at the beach or sightseeing. Evenings on the islands are wonderful. Everyone goes out for stroll, browsing in shops or sitting down for a drink. Dinner is a relaxed affair, an entertainment in itself. Try a different restaurant or taverna every night if you wish, or return to your favourite and be treated like an old friend. You can easily spend hours at the table sharing different starters between yourselves, ordering another carafe of wine, and taking your time finishing.

If you still have the energy, nightlife begins in earnest around midnight, and goes on until dawn. By then I am tucked up in bed, so miss out on that last activity.