this past summer we stayed at the state park in the diamond state park. Not all sites are pull thru most were back in. Make advanced arrangements if you can, we lucked out a reservation was not filled and we got the spot. pretty nice place, the diamond search we did not do due to all the mud from the rains they were having. Lotsa folks tried seem to have fun but we never did see any 'finds'. we stayed at the KOA in hot springs, pretty nice place good folks to deal with it seems. again many back ins. as to the hot springs themselves, no public springs just hot baths in spa's. They do have some good free hot water/mineral fountains to get drinking water from. Take some jugs to fill ($1 ea locally).
just out side the diamond park there are 2 I think rv places, the park was better IMO. Getting there from the interstate you can 'visit' klintons home, the parking lot was empty when we drove by.