Buy the Butler Maps for the Ozarks
That will give you a really good guide to the best roads. Decide where you want to ride, and then decide where you want to stay.
I second the approach of connecting certain dots to maximize your quality time in the saddle. Eureka Springs is a superb jumping off point though, as AZ Jim and others have mentioned. You may want to add another overnight destination though like Russelville, Hot Springs or Mena to give you access to the other half of what the Ozarks have to offer. Connecting the dots will provide you with some of the best riding in the country. Here are my favorite highways, with towns (and a few state parks) serving as the "dots", favorites mentioned first:
- AR23 (aka pig trail) from the Missouri line south to Cass (side tripping to Crescent Hotel in Eureka and to War Eagle Mill south of Eureka along the way), then AR215 to the Oark general store (great atmosphere and burgers); then back track to AR16 east to Swane; then AR21 to Boxley and AR74 to Ponca and on to Jasper. This will be the junction with "Scenic" highway 7.
- Arkansas Hwy. 7 is right up there with the pig trail, possibly better. From Jasper head north if overnighting in Harrison, otherwise head south to Russelville and continuing all the way to Hot Springs. There, find the Arlington Hotel and take the side street off AR7 beside the hotel up the incredibly winding switchbacks to the top of Hot Springs mountain. This drive is a museum piece road. Hot Springs has a few great BBQ joints. I usually do a hot bath while there if overnighting.
- The next ride connects two of the state's best parks, Petite Jean and Magazine Mountain. Backtrack on AR7 north, then take AR9 to Oppelo, then left on AR154 up and over the first mountain park, checking out the CCC cabins & lodge en route. Then take AR10 to Havana and launch onto AR309 up and over Mt. Magazine, which has newer/pricier lodging. Wait to eat when you're good and hungry in Paris at the Grapevine restaurant. Well worth it. In fact, Paris would make a good overnight.
- AR27 is another while you're in the area. Backtrack from Paris to Dardanelle, then take AR27 south to Norman, Caddo Valley and Glenwood. Glenwood has a cool golf course with overnight accomodations. Then head west to Mena and take the Wilhelmina scenic drive into Oklahoma.
- One other state park worth checking out for their CCC cabins is Devils Den State park, off I-49 north of Fort Smith. The entrance road to this park is magnificent serpentine & hasn't changed in 40 years. This at least gives you some other overnight options with terrific roads thrown in for fits and giggles.