Close to town looks at Ramon's, Sun Breeze
Map of the town area:
//ambergriscaye.com/pages/town/mapdowntowndetail.html#heart
AC is the diving home base. You can get any where from there for diving. There are great resorts on some outer atolls but there will be no shopping, I do not know about pools also.
AC offers (to me) basic diving. The currents are manageable and Turneffe and others offer some of the best Caribbean diving. I've yet to have a better night dive than in AC.
Look at Placencia area. I've not been there but it offers diving and jungle reserve.
Here's a trip report. By the way, to dodge the "golf cart traffic" walk 50 yards away on the white sand beach! I didn't notice that much traffic compared to other places. Far from Cozumel or the eastern Caribbean islands.
http://www.belizeforum.com/cgi-bin/ultimatebb.cgi?ubb=get_topic;f=10;t=000563
Maybe we'll run into each other.
Bob