Yeah, get with me and/or check out the Arkansas Crawlers. http://arkansascrawlers.com/
I don't know all the backyard public-land trails - only a few of 'em, but I know the people who do. Probably faster though just to ask people on the forums over there.
Can certainly show ya around Superlift ORV park in Hot Springs. That's where I do most of my wheelin', and always happy to meet people there and go wheel with 'em.
Our club, the Arkansas Crawlers, actually have a New Guys event coming up March 5th there at the ORV park with full guided runs for various levels of difficulty. I'm one of the regular guides for the park and our club.
But to list a few other big places...
Of course... Superlift ORV.
Byrd's Adventure center
Wheelin' World by Eureka Springs (Newest orv park)
There's a nice highline/powerline trail west south-west of little rock
By the Saline River off I-30 there's a place people play in the dirt/mud
Around Gravel Ridge there's a trail, though I've never gone and done it.
Rock Creek (Booneville)
Ya, there's a ton of trails to explore. I don't know very many though.
Other big destinations nearby Arkansas
Disney OK - awesome wheelin' destination at Hogan's offroad.
Clayton OK - some hardcore stuff
SMORR, Southern Missouri Off Road Ranch
Katemcy rocks in Texas
There's a lot more, but getting tired of trying to think of 'em all. Where in Arkansas are ya at?
Edit: Ah, Searcy. So not too far from me.