This is my favorite place to camp if you want close to the actual town of Hot Springs. It is part of the National Park system. It is in Gulpha Gorge and is really beautiful along the creek. It is a first come first serve park. No reservations taken.
Gulpha Gorge Campground is located off US Hwy 70B on the east side of Hot Springs. For GPS directions, the physical address is 305 Gorge Road, Hot Springs AR 71901.
It has restrooms but no showers. $24.00 per night unless you have the Golden Age pass, then it is 12.00 per night.
http://www.nps.gov/hosp/planyourvisit/campground.htmLarry