This may be more than you were looking for, but this orienteering club meets at Oak Mountain:
http://www.vulcanorienteering.org/index.php?page=home

Found that looking for orienteering courses at Oak Mountain. They offered those some years ago, as I recall.

Check out Cheaha, Sipsey Wilderness/Bankhead for places to hike and camp. I went to Little River Canyon last week, and it was great, but I think there's no overnighting in the canyon itself, and there's not many trails. One goes from Eberhart Point to the canyon floor, and then you can go either way along the river I suppose. Oak Mountain is fine for checking out gear, or a few overnighters, but gets old quick since there's not a lot to see or do there. Used to go to Sipsey with friends from that area, and am going to check out a couple of trails at Cheaha this week, maybe Wednesday. Tons of places to go for dayhikes around here, too.