Bull Shoals Lake area has some nice trails.
This is the trail right by the lake in Lakeview. http://www.swl.usace.army.mil/parks/bullshoals/hiking.htm
The State Park that is on the White river also has some trails. http://arkansasstateparks.com/park-finder/hiking-detail.aspx?id=8
Gaston Wildflower Garden Trail
Time: 1 Hour
Description: This memorial wildflower garden loop trail meanders through three acres of wildflowers that change each week through the season. Wildlife, including birds and butterflies, can be throughout the trail at feeders and rest areas. The area is under constant development amd memorial contributions may be made at any time.Location: From Mountain Home, travel six miles north on Ark. 5, then go eight miles west on Ark. 178. Or, from U.S. 62 at Flippin, travel 10 miles on State Highway 178E to the park. Bull Shoals-White River State Park, 153 Dam Overlook Lane, Bull Shoals, AR 72619
Big Spring Park has two circular 1/2 mile walking tails and a 2 mile trail all along the banks of the White River. Take your swim suit as they also have a cold fresh water spring with a rope to swing into the pond.