Petit Jean State Park is one of the best state parks in Arkansas simply because it has such a variety of landscapes and things to do. The park is based around Petit Jean Mountain and the rugged bluffs that tower over the Arkansas River and Cedar Creek. Towards the top of the park, there' an artificial lake where you can go fishing or try your hand at kayaking or paddle-boating.
The reason I like Petit Jean State Park so much are the rock formations you can explore. The most famous rock formation in the park is Bear Cave (don't worry, there are no actual bears in sight!). After hiking about 30 or 45 minutes, you arrive at a system of passageways and grottoes that you can explore. Or, try the Seven Hollows trail which take you under one of the coolest natural rock arches I've ever seen.
Finally, don't miss Cedar Falls and its stunning 100ft. drop to the canyon floor. There are several trail that lead to Cedar Falls and if you have any doubts, just ask one of the park rangers. It's the most popular park of Petit Jean State Park so you won't have any trouble getting there. Also, make sure to have a look at the park's website as they organize group hikes, Native American themed activities, and all kinds of other events on a regular basis.