I love cheap trips to the Keys..... I've tent camped at Bahia Honda, Curry Hammock and Long Key State Parks. All are nice, though Long Key's sites are pretty close to the main road, so bring ear-plugs or a fan to drown out the sound with some white noise. All have electric hookups so you bring extension cords to charge your phone or computer or camera batteries.
In theory, you can dive off the beach just about anywhere, but you're not going to see much and it will pretty much be a sand dive. Bring a dive flag if you decide to try it. All the diving in the Keys is basically boat diving with the only half-way acceptable exception I can think of being Cannon Beach in John Pennekamp State Park and from descriptions I've seen posted, it doesn't sound very nice. I know Pete, the owner of SB, has posted a couple reviews of his dives there: search the Florida section and you can probably find his posts. I've read about diving at Bahia Honda that tomfcrist referenced but have never tried it, I've read that local knowledge of the currents/tides is critical or you can be pulled out to sea very very easily. Just watching boats drift fish from the bridge overlook, one can see how swift and potentially dangerous that current can be.
Another cheap option for accommodations is the Hungry Pelican Motel on Key Largo: they have one room that is tiny tiny tiny that rents for $60 a night and a couple of tiny tiny rooms that rent for $65 per night. I've used these options twice, its not much more than camping, but you'll have a fridge, shower/bathroom, a/c and comfortable bed and only spend another $20-$25 per night over a camp site.
