Byrd's is in a nice area. I haven't been on the trails in a long time there, but I remember them as mostly Jeep trails.
It's right on the Mulberry River, which great for canoeing. It's really near Cass, Ozark is 20 miles or so south of there. You'll also be very close to the Mill Creek OHV area. http://www.riderplanet-usa.com/atv/t.../ride_8b75.htm
I've never camped there, so I cannot comment on those services, but the whole area is nice, as far as the Ozarks go. You would also be only minutes from Oark General Store, which was opened in 1890. http://www.oarkgeneralstore.com/home.html
It's a really popular place to eat and they have good food. The drive there is scenic and it really is a destination worth visiting. There's typically a crowd of motorcycle riders of all types there, as the ride there is that nice.
Then there is Turner Bend just around the corner. http://turnerbend.com/ They have canoe rentals and cabins, sell fuel, beer, and other typical small store items. Be sure to buy a Pig Trail (Highway 23) sticker if you stop by.
Another place to camp or lodge is Mulberry Mountain, which has trails that connect to Mill Creek. http://www.mulberrymountainlodge.com...do/atv-trails/ That is where the now defunct Wakarusa music festival used to be held. http://www.wakarusa.com/
I used to live within minutes of those places and rode my trike all over the place. It's been a while since I have though. I mostly buzz through on dual sport bikes now, being street legal really opens up riding opportunities.