Being a jeep owner the Superlift Off Road Park bar none is a good reason to visit. You can camp there on your way thru and visit Hot Springs just next door at night.
We moved just north of Eureka Springs 4 years ago. If you like old cars there is a car show within a hours drive up here every weekend plus cruise nights on Friday and Saturday nights..
The outdoor adventures as everyone has mentioned are just epic. You can also skydive over the Ozarks. And that's a neat experience. Along w/ skydive near Little Rock at night and that is pretty neat to see the river at night and downtown lights.
I used to be an over the road truck driver and let me tell ya, i've been through almost all 50 states and Arkansas is by far one of the most beautiful. The Hunting and Fishing are also first class.
Lived here for a bit over 2 years now, and am about to move away. However, it is its a great outdoors state to visit. I can't say much good about many of the Cities compared to others.
Someone mentioned trout fishing on the Little Red River in Heber Springs. There is also a HUGE lake called Greers Ferry Lake that you can fish. Fantastic hybrid fishing right now. Plenty of bass and brim too! You can schedule a guide or rent your own boat. There are plenty of things to do around the Heber Springs area; hunting, fishing, hiking, camping just to name a few.