In Southeast Florida, you can lobster hunt off just about any charter boat north of the Keys. Some of the Keys boats will also go to sites outside the protected zones but you have to call ahead to make sure that's the case. On most dives in Jupiter, which I did with Jupiter Dive Center, I'd usually came back with a couple of bugs and I'm a casual hunter. Really focused divers limit out much of the time. One thing to note in Palm Beach County, bugs normally are found in ocean topography that isn't very pretty. So if you aren't finding bugs in the normal hiding places or just pulling out shorts, you won't be able to have the pleasure of a beautiful reef dive.
I've also had luck on Pompano's shallow reef line with South Florida Dive HQ.
The best site I've hunted on in the upper Keys is Conch Wall. It's a deeper reef that doesn't get hit by many charters all that often. Conch Republic Divers hits the reef semi-regularly.