It depends on what you are looking for.
For an out in the country atmosphere that is still convenient to Little Rock there is the Corps of Engineers' Maumelle Recreation Area & Campground located near the Murray Lock and Dam. Here's a link to a general description of Corps stuff around Little Rock: Arkansas River Between Little Rock and Dardanelle
. It's a nice campground with 144 sites and is located at the west end of the extensive Little Rock/North Little Rock bike path system. Here's a link to the Corps' site about the area including links to thier reservation system: Corps Lakes Gateway: Arkansas - Arkansas River - Murray Lock and Dam
For more of a downtown atmosphere, North Little Rock has a very nice campground right on the river near their downtown entertainment and dining area at the east end of the bike path. It's just across the river from the Clinton Presidential Library in Little Rock which is located by Little Rock's downtown entertainment area. The Library is accessable via a retired rail bridge converted to bike and pedestrian traffic as well as convenient auto routes. See Downtown North Little Rock Arkansas Riverside RV Park
Tere's also a KOA in NLR, but it's not as nice as either of the other locations. It is, however, near the west end of the bake path by the Murray Lock and Dam, so it's not totally just an Interstate rest stop.
There is other camping nearby, but these are the main LR/NLR ones.