BHB is an easy dive, but only at slack high tide: here's some general info:
Blue Heron Bridge
I agree that Lauderdale by the Sea is a good beach dive option too: here's some info:
http://www.scubaboard.com/forums/florida-diving/290550-lauderdale-sea-beach-dive.html
One of my favorite shallow dives in Pompano is the Copenhagen wreck and the reef around it: here's some information
http://www.museumsinthesea.com/_docs/Copenhagen_brochure.pdf
If you plan to beach dive a lot, join this club:
Gold Coast Scuba Divers (954) 616-5909 (Fort Lauderdale, FL) - Meetup The shop also sponsors boat dives in the area too.
Try a number of different boats to see the ones you like. In Pompano, I like South Florida Dive HQ, Pompano Dive Ctr and Scubatyme. There are plenty of others too. Gold Coast and Force-E are good shops in that they can arrange dives on a number of different boats if you describe what you are looking for. Force-E has a shop in Boca.
After a few dives, if you want to try deeper drift diving in a relatively safe setting, check out Scuba Club in WPB. They put several DM's in the water and typically have a DM that stays with the air divers and one that stays with Nitrox divers.
Once you have a few more dives under your belt, get Nitrox certified and come up to Jupiter for some big marine creature dives: I like Jupiter Dive Center.
BTW: I've done training with Jupiter Dive Center, Scuba Club and Gold Coast and all were top notch.