I'm not up on where to go dual sporting and such in that area. I live in north central AR and you're just a short way from some great paved roads.
Head towards Ozark, AR from Mt Magazine and take Hwy 23 north to AR 215, head east to Oark and have a great meal at the Oark General Store. Go back out 215 to 103 and head south into Clarksville. From there you can follow a variety of roads back to Magazine.
Shirleys Outback (no affiliation with the chain) is just north of the park, has good food, and is moto friendly. There's also a great mexican restaurant on the south side of the river in Ozark.
Make a ride up Hwy 7 to Jasper and eat at the Cliff House Inn, just south of town. Or ride into Jasper and eat at the Ozark Cafe, which has been in business since 1909.
Have a great trip.
Jay
We did... 2 weeks ago. I WISH we'd have had that info at the time. Thanks much.

Now I'm hungry.