I'm currently staying at a campground in Withlacoochee State Forest near Inverness, FL. This particular campground has water, electric and a dump station and is $20/night. It's a bit "dated" with older , fixed in place picnic tables but still pretty nice. Only 2 miles from Inverness which has nice grocery stores, restaurants, laundry etc. There is also primitive camping available for $10/night. There are hot showers and flush toilets as well. They do not take reservations. It was about 80% full over New Year's but there are only about 4 other campers here and about 27 sites total.
More info can be found here-
Recreation at Withlacoochee State Forest / Withlacoochee State Forest / State Forests / Our Forests / Florida Forest Service / Divisions & Offices / Home - Florida Department of Agriculture & Consumer Services
There are a few hiking trails but not much else. Seems popular with locals as well as hunters.