Rugrat, last year we spent four weeks touring the state and 30 days at a campground in Lakeland.
We started off at a great campground just north of Jacksonville in Atlantic Beach FL - Hanna Park. Spacious sites, lots of trees and reasonably priced.
Won't mention all of the campgrounds that we visited as they were only for two-night stops, but besides the one in Lakeland, the best two that we found were:
Everglades National Park (if you are at least 62, get a golden age passport for $10 lifetime and the park entrances are free and camping is half-price) - Long Pine Key Campground (was the only campground open last year, due to hurricane damage at the other one). Only problem is that there is no power and water and sewage is available only at the sanitation station. Sites are huge and they have fire rings at each site (rare for many Florida campgrounds). Great interpretative center a couple of miles away - saw about 200 gators plus a lot of other wildlife in the evening and daytime visits to it.
Fort DeSoto Park, near Clearwater - absolutely beautiful, but it may be too late to get reservations. One of the best beaches I've been on and the sunsets are among the best. You've got to see this park to believe it.
Finally, in Lakeland, we stayed 30 days at Tiki Village, right at exit 32 on I-4. Even though we were close to the expressway, the park was quiet. I believe the price this year is $475/month for stays of at least two months. Park is four blocks from the Lakeland Square Mall, lots of eating places nearby and about two miles from Joker Marchant Stadium where the Detroit Tigers train in late February and March. That's where we are headed for 2 1/2 months this year.
Hope this gives you some ideas.