Howdy fellow Louisianamite. Many of our state parks are good and fun places to stay. I don't know which ones were possibly damaged by the recent flooding in your area though.
Up here in the NE part, I really like Lake Darbonne SP, Jimmie Davis SP, as well as Lincoln Parish Park.
Here is link you may want to peruse:
Although a pretty good drive from your base of operations, everything around Hot Springs Ark is good. Lake DeGray SP, Lake Catherine SP, and Lake Ouachita SP are all excellent, but you have to make reservations for any of these well in advance as they book out. DeGray and Catherine even have horse rentals.
You might also want to look into MS and see what they have available close to you, but I have no experience with south MS parks.