We've visited the FL Keys and Key West so many times we've lost count. If you're a first time visitor, just the drive from Key Largo to Key West is a treat. A drive like no other in the US.
Commercial RV spots in the Fl Keys are pricey---typically $100-$150 a night (some like Bluewater even higher). The best overall value is the Bahia Honda State CG's with a number of scenic tree-lined FHU sites right on the water for only ~$40. Unfortunately, they're typically booked up solid almost a year in advance. There is no one "ideal" RV park in the FL Keys---there are major pros and cons to all (price, availability, location, accommodations, etc.). To my knowledge, there are no public RV parks located on Key West (NAS KW CG is currently closed due to Covid). However, there are several located on Stock Island (less than a mile from Key West). High tourist season runs Dec-Mar. IMO, you can get a very good feel for what each offer by visiting their websites, viewing the premises via satellite and reading reviews.
If you can find accommodations for your camper, I'd say a visit to the Fl Keys would trump a trip to the panhandle. The panhandle's nice, but IMO it's more or less a replay of the entire eastern seaboard.
Good luck!