Depends what time of year you want to go. As neil Down says there are loads of 7 day caribbean cruises, however some people don't want to fly that far just for a week. if you prefer a shorter flight to join your ship, the the Eastern or western med are good destinations as long as you are going between May and October otherwise might not be that hot. All the cruise lines operate there. To help narrow doen your search decide whether you prefer acruise with some formal nights or prefer something more casual. Also decide whether you prefer most of the other passengers to be Britsih or would prefer a mixture of different nationalities. The 2 Italian cruise lines MSC and Costa have a younger age group than some of the other companies. Whatever you pick and wherever you go, I'm sure you'll have a fantastic time. most people enjoy their first cruise the bes.
Ocean village is really good for first tme cruisers and is aimed at younger market so theres more nightlife.
My first cruise was on Royal Caribbean and the nightlife and atmosphere was fantastic. They have some good 7 night cruises around the Greek Islands and Med.
There are loads of 7 day cruises in the Caribbean, fly out Saturday back home Sunday week. ok 8 days Neil Dow.