You'll find Caye Caulker rather cheaper for what you want. Dr Bill suggests Belize Diving Services and I endorse that. The main alternative is Frenchies. Either will probably be able to do the local dives you suggest - as the diving in front of CC isn't great they often come up to San Pedro to dive. A 3-tank may be difficult though certainly you'll manage a 2-tank.
From CC only Frenchies or Big Fish take boats to the BH, but you don't need to have dived with them the previous day - whoever you dive with will arrange it for you. Additionally, AquaDives from San Pedro also pick up at CC on BH outings and charge the same.
On AC you'll find much more choice for local diving. Ecologic towards the northern end of town is one choice, my own near the center of town is of course another, but there are several others that will do you as well. For BH trips your main choices are Amigos del Mar and AquaDives. If you're a nitrox diver it makes sense to use nitrox for the second and third dives of the day, something Amigos provide and AquaDives don't. There are a couple of other choices but I'd stick with these two. You'll pay around US$50 more for a BH trip from AC compared with CC, simply because of the extra fuel used.
If you stay on AC (and Pedro's is a good budget choice) you'll find it easy to do a 2-tank trip outside the reef in the morning and experience the swim-throughs/tunnels etc, and a combined dive/snorkel to Hol Chan and Shark Ray Alley in the afternoon. You may find them as easy to organise from CC but I'm not sure.
The standard BH day contains three dives - the first in the Hole itself (140' or so) in the center of the atoll, the second a wall dive just off Half Moon Caye in the SE of the atoll (90'), the third another wall dive ending at the Aquarium (50', just off Long Caye).
Renting gear is no problem, nor is finding a wide range of available accommodation. There will be no problem organising your morning local dives, but the afternoon trip to Hol Chan will probably depend on there being a few other people wanting to go. And it is a very quiet time. The BH trip is wholly dependant on their being 8 or 9 other divers wanting to go, and at that time it certainly won't be the case every day. It's probably best to do your local dives with a helpful dive center that doesn't run its own BH trips, as that way they'll trawl around to try to find you a trip. If you're on AC you won't be able to get on one of the CC trips. If you're on CC you will be able to catch an AquaDives trip, and I imagine Amigos could also be persuaded to stop if they're going. Make sure that these operators are asked if they're going, as otherwise they probably won't be asked.
Overall for this trip at this time I think you'd do better to stay on CC and dive with BDS. I can't suggest accommodaton - email BDS and ask for their recommendations.
