Tips from a Local:
Bahia Honda fills up WELL in advanced because it has the conception of being one of the only campsites in the keys really. I love Bahia Honda but if it is full here are some other places to check. I will try to keep them in order down the Keys.
John Pennekamp Coral Reef State Park is in Key Largo and is an AMAZING coral reef for diving and snorkeling. They have a glass bottom boat as well if swimming isn't for you.
Long Key State Park is between Islamorada and Marathon, nice hiking trail and fishing here.
Sugarloaf KOA is on Sugarloaf. It actually has Airstream trailers you can rent. They also have a dog park here! Its about 1/2 North of Key West.
Geiger Key Marina. This is actually near my house and I often go here for onion rings

The food here is tasty and on Sunday they do a BBQ which is good. There is paddle boarding and kayaking. The view there cannot be beat. The turn off of US 1 is at MM 10.5 so you are very close to Key West. I live at MM 10.5 and commute by bike to work! There is a bike path the whole way from US 1 into Key West.
And lastly there is Boyd's Key West Campground..like the name implies it is in Key West. There are waterfront sites and a boat ramp. Can't say I know much about this because I have a house on the water here so no need to ever go!