Bear Creek (Franklin/ Marion Co.)

There is a campground about 10 miles from the Bear Creek outfitter, called Rock Bridge Canyon Equestrian Park. They have basic tent sites for $10 a person per night with a very nice, clean bathhouse. They also have camper sites with hookups for $25 a night.
There are several trails on the property that you can hike, and the lady who runs it can give you maps and information.

http://rockbridgecanyon.com/

Be aware that there are no restaurants nearby except for a diner in a shell station, and it doesn't serve food on Sunday.