For newer divers, Key Largo and Islamorada are both great places to dive. Lots and lots and lots of shallow reefs and a few shallow smaller wrecks. There are a few mid-depth reefs as well (60 feet) and a couple of deeper reefs (100 feet). The four deep wrecks are also relatively easy to dive (especially the Eagle and Spiegle Grove) if current isn't bad. As an experienced diver, I really enjoy going to the upper Keys for both the diving and because of the vacation vibe that permiates the area.... lots of tiki bars and restaurants. While driving over that final bridge to Key Largo, I can feel all of life's stress drain out of me!!!!! The History of Diving museum is also in the upper Keys and something fun to do if marine conditions don't allow diving.
I have family in the Jupiter area and dive there frequently when I'm back in the town. Its all drift diving, a bit more advanced but still much fun. The reefs aren't as pretty as they are in the upper Keys, but the likelihood of seeing large marine life is fairly high (sharks, goliath grouper, turtles, big green eels, etc.). If you want to see Lemon sharks, Feb is usually a good time to dive in Jupiter since they are migrating through and gather at a few sites that dive operators will go to regularly. In Jupiter, its helpful to be Nitrox certified since the depths will keep dives for air divers pretty short. Like Norrm said, AOW is also helpful.
A few operators I like:
Upper Keys: Conch Republic Divers, Quescensce, Rainbow Reef (particularly good for new divers since they put guides in with all divers)
Jupiter: Jupiter Dive Center