I would suggest staying away from bigger highways like US65, US412 and US62, because they get more of their share of traffic and enforcement.
Also, a highway's number doesn't mean much without specifying between where and where else. For instance, AR9 from Melbourne south to Allison is as much fun as you can have with your pants on, but AR9 from Shirley to Clinton is a yawner where you'll be able to memorize all of the bumper stickers on the back of all the Subarus and Altimas in front of you.
The backroads like the ones mentioned by Ed are no fun in a cage, but really fun on a bike, so the locals and work trucks tend to go for the bigger roads and leave the good ones to us. And even if you don't want to get all sweaty, you can just throttle down on the good roads, because the scenery is nice too. As rural as it gets.
I love the Smokies, but I find a lot of the best roads there are covered with driveways and other vehicles. On some of the best roads in AR, you can find yourself feeling like you're riding after the rapture. I love that.
I would suggest the Mountain Home area way above Eureka Springs for pure riding reasons. You have to ride a pretty good distance out of Eureka Springs to get to fun roads. Now, Eureka Springs does have a lot of kitschy touristy stuff, if you like that sort of thing. Magic crystals that can make your hair grow and stuff like that. Folk music too.
Make sure you post a date, if you'd like some company. I love riding down there.