You've got options:
Ambergris Caye - this is probably by far where most divers/snorkelers/beachcombers go. Advantage: lots of choices with respect to accommodations, dive ops, food and night life. Disadvantage: it's an island, so if you're planning to work in mainland stuff like jungle hiking, mayan ruins, cave tubing, etc, you'll have to deal with the logistics of getting back and forth to the mainland. It's not hard so much as time consuming. Another disadvantage may be dealing with crowds, especially if you go in high season.
Turneffe Atoll - there are several "resorts" out on the atoll. The big three are Turneffe Island Resort (stayed there twice), Turneffe Flats and Blackbird Caye Resort. All-inclusive and pricey but not terribly so if you take into account everything's paid for. Advantage: these places are like summer camp for adults. Great diving within minutes of the dock, good food and lots of relaxation. Disadvantage: even more difficult to do anything on the mainland, no night life to speak of.
Placencia - Not as big and popular as AC, it's an interesting mix of tourism meets fishing village. Again, lots of choices for accommodations and food. Only a couple of dive ops to choose from but Splash Dive Center there is excellent (used them twice). Advantage: even though it has a definite island vibe Placencia is actually a peninsula. The mainland is a quick drive up the one and only highway. Adventures abound. Disadvantage: the boat ride out to the reef and back is longer, about an hour each way. Not much of a disadvantage if you like boats, which I do.
There's also Hamansi, a resort up the coast from Placencia in Hopkins. I haven't stayed there, but I've seen it. Looks nice and enjoys an excellent reputation.
And Hatchet Caye, another inclusive resort about a half hour off Placencia. Haven't stayed there either but I've passed by it a number of times on my way to the Silk Cayes. Looks nice and is supposed to have an ultra-light fixed wing but I've never seen it in action.
There are probably more, but I think I hit the highlights.
And, of course, there's always a liveaboard.
As you probably know, the "bucket dive" is the Blue Hole. Somewhat controversial, at least here on ScubaBoard, you should probably read the threads on it before making up your mind. From AC, it's about 2.5 hours each way and is an all-day trip combined with some really great diving in the area. From the atoll resorts it's more like an hour each way and is also an all-day trip combined with the same great diving. From Placencia, Splash runs a two-day trip, diving along the way up and back with the BH being the first dive of the second day after spending the night on a nearby caye.
Belize is a fantastic place to visit and dive. I'm sure you'll enjoy it. And while it's a small country it's still a big place. I don't think you can see the best of Belize in a one-week trip. But that doesn't mean you can't try, lol.
) Swash, the water was very clear, calm and diveable. 
