Plenty of great riding in the Ozarks. I've done it at least 7 times and will likely be back there again this year and many more times.
Just a few thoughts off the top of my head:
1. Harrison is better to base out of (motel or camping) than Eureka Springs. E/S is more congested, more touristy (er... touristy trappy), the food is not as good, the bikers are mostly pirates (in every sense of the term), and overall MUCH more expensive. There are campgrounds near Harrison that will accommodate you need to pre-ship your gear.
2. From either location though, you can create several (3 or 4) nice loops through the mountains and hit all of the great roads. More on that later.
3. If you are planning more than 4 days in Arkansas, I would suggest you venture south of I-40 and check out some of the great riding in the southwestern part of the state. The Mena, Russellville, Lake Ouichitta (sp), and Hot Springs areas have some great things to see and ride to and from. But all of that is too far to do in a one day trip, especially from Eureka Springs. So as an idea, you could make a one night reservation at one of the lodges Redfish Hunter has suggested (Mather Lodge in Petit Jean State Park would be my first choice), and take a break from the tent.
4. Go to the Oark Store and eat breakfast or lunch. Take your time - trust me, it's cool.
5. Roads you simply cannot miss:
- Hwy 7, preferably in its entirety, but absolutely do not miss riding from Russellville to Jasper (or visa versa). If you catch that road dry and clean in the mid morning, it will be a spiritual experience for you.
- Hwy 341, AKA Push Mountain Road, eat your Wheaties for breakfast, and just before you get to the base of the mountain, downshift twice and tell your sweetheart to hold on. Holy cow - what a great FJR road that one is.
- Hwy 74 between Piercetown and Ponca. Stop at the Elk Center in Ponca and take a walk down the path at the Lost Valley water falls.
- Hwy 123 between Jasper and Hagerville. This one is 50 miles of 4th gear rollercoaster. It's wonderful.
- Hwy 16 between Hwy 23 and Deer, AR. Take a walk at Alum Cove to see the natural bridge.
- Hwy 27 between Big Flat and Dover. Not many people know about this one - it's very curvy in spots, very good pavement, few road side waterfalls, and just beautiful mixed scenery as you go in and out of the forest and see the farm valleys. This is a great ride
- Hwy 23 (aka The Pig Trail) between Hwy 412 intersection and Eureka Springs. I hesitated on this one - frankly, I don't care for the Pig Trail too much. It's usually full of pirates that don't know how to ride twisties, the road is broken up in sections, and although it is very curvy and scenic with the tree canopy over the road, quite frankly, the other roads above are all better IMO. But its kind of like the Dragon in North Carolina/Tennessee - since you are there, you kind of want the right of passage. And like the Dragon, if you forced me on the Pig Trail, on a decent weather day, I'd run that early in the morning before the pirates get up and start belching all over the place.
This is just a start, there are many others I can suggest. I can also suggest some "off the bike" things to do, such as Hiking and sightseeing. Let me know if you need additional help.
Also, as RFH suggested, I have some routes on my ride reports from Arkansas - here is the one from last year:
https://www.fjrforum.com/forum//index.php/topic/162607-steep-crooked-and-the-shiny-side-up/?hl=+steep++crooked++shiny
Hope this helps, cheers!
