Where and how should we organize for 2 or 3 days of SCUBA diving on a 9 day trip?
Ambergris Caye has the most infrastructure and plenty of dive operators, it's a fairly busy place but still tranquil enough and plenty of dining options. Caye Caulker is smaller and a little more secluded.
I really enjoyed South Water Caye. It's towards the southern end of Belize's offshore Caye system and is a pretty small and remote island. If you're serious about wanting to dive, dive, dive - you'll have the reefs here largely to yourself and no wait for tanks or boats. Also the reef just off the beach is amazing and as there are no crowds, you can explore it all day without a bunch of bungling tourists kicking you in the face with their flippers! The down side is there is really not much nightlife on the island. The handful of resorts each have their own bar and dining area, and I believe there is one additional independent cafe/bar. So, this is a great place to get away and get underwater, not so great if you're really looking for a party holiday...
One more word of advice, before you worry about booking dives, choose the island that interests you the most and reserve a spot at a hotel. The dive charters work directly with the hotels, so once you're set on a spot, the rest of it (getting there, charters, etc.) falls into place fairly easily.