TN State Parks: Reelfoot Lake State Park
We have visited here a few times and camped here ourselves the last weekend of July. We paid $25 a night for a waterfront site. The roads are decent and the sites are pretty level and wide. The bath house is nice and clean and the showers are very hot. Campers have access to the swimming pool at the Air Park. (There is also a second park over by the Air Park that is open year round.) Also note it is 50 amp hookups.
There is plenty of room for the kids to ride bikes and the squirrels are somewhat tame and will even eat out of your hand at times. Do keep your trash picked up and watch your food though because there is a raccoon who scavenges the park for food after dark. There are a lot of regulars who camp here and they are all very friendly people.
In the area, there are a few things to do. We always walk the boardwalk and tour the museum at the Visitor's Center. There are also eagles, hawks and owls behind the center. They have boat cruises that are very inexpensive and a lot of fun. The one hour tour is great for kids but the three hour trips would probably be too much for little ones. If you're into photography, there are great photo ops of the sunset over the lake and wildlife in the area. Of course there is fishing!
We enjoyed this park and would definitely recommend it.