Capt. Rob;
A lot depends on what you want to do in your non-diving time. Belizian Shores does have the nicest pool on the island and (assuming they fixed the heater) a nice swim up bar. The units are very nice and large and comfortable. On an island not known for great beaches, theirs is not too bad and they do have complimentary use of the kayaks for guests. The location is not, however, great if you want to party at night. While there are water taxis, they don't run late at night and thus limit your bar hopping to the one on site and perhaps Captain Morgan's down the beach.
You should look at the island map on the website suggested by Peter. The island basically consists of three main areas....downtown, north of the cut and south of downtown. Everywhere in the downtown area is easily walked and this will offer your best choice of restaurants, bars and nightlife. South of downtown has hotels that are close enough to walk to and from or be reached by a land based taxi that operate later. North of the cut has properties that still require a water taxi because, in spite of the new bridge, the roads can be quite rough.
Downtown the Sunbreeze is a great choice and has a dive op that has a good reputation (Aqua Dives) but you should be aware that you can use any dive operator and there are several who get great reviews here on ScubaBoard...including Peter at Pro-Tech who never blows his own horn here. I have used his services and highly recommend him. The Sunbreeze is a U shaped hotel, wrapped around a center pool and facing the beach.
South of downtown there are a number of good properties including Banana Beach and I have stayed there and it was very nice. All the dive operators will do pick-ups from there and they have a couple of pools and a beach that is not too bad.
The closest you will find to a dedicated dive resort on the island is Ramon's and it is a nice looking property and a long established dive operation. Based on my stays on the island, my guess is that you will find the highest percentage of divers at hotels such as Ramons, The Princess and the Sunbreeze...mainly because all of them get marketed as dive spots. Places such as Belizian Shores and Banana Beach would have fewer divers.
I have stayed in the North, in the South and downtown and probably preferred the downtown and south locations because they offered the greatest close by options of dining choices. Up north, in spite of the fact that there are outstanding restaurants, you do need to take the water taxi to enjoy them and that is not always convenient.
In the end it all depends on your vacationing style and how close to town you wish to be. You will be able to dive from any property on the island although some may charge extra to pick up further north due to fuel costs.