I haven't tried it yet, but I'm told there are some trails at se59th & s Douglas, just east of Tinker. If you look at it in GoogleEarth its just a dirt road coming off se 59th. I don't know the legality of using it, but there are no fences (at least according to when the googleearth images where taken).
I chatted with one local (yukon) jeep guy in a parking lot. He said he just wheels somewhere outside town. He didn't specify where. I assumed it wasn't an authorized area.