I took my granddaughters (when they were 6 and 7) to Petit Jean State Park, SW of Morrilton AR, and they totally loved it. This could be a good day trip or a place to camp (we camped under the pines).
This place has some great trails. The Bear Cave trail is pretty short and it winds through tall rocky outcrops; the kids could play hide and seek in here quite easily.
There are a couple of waterfalls, including Cedar Fall which you can see here. One can hike to the foot of the fall or view it from above. On the hike from above, the kids will love climbing on the turtle rocks (the outcroppings look much like turtle shells).
One can also hike or drive to some splendid overlooks:
They have a little amphitheater with evening talks given by Rangers, explaining things of interest (like the legends of Petit Jean). And of course there is a nice playground area; kids always love slides and swings. One other advantage to this place is the slightly higher elevation, which means perhaps 5 degrees cooler temps.