I don't know why people told you not to fish at Oak Mtn. There are four separate lakes there and I can attest there are bass in all 4! Now I have not fished there in a couple of years, but it used to be good. Gets a lot of bank pressure though. Also as for shore line, there are miles and miles of trails around those lakes. You have to be willing to hike though. Here is one place to go:
Go to the picnic area it is a turn off of the main road. You will know you are in the correct area if you notice a field with a rappelling tower and on up the parking lot toward the back there is an old bmx track. Across from that track is a gate, and down the road a bit beyond the gate is a lake that is where the cabins sit. (You can drive to that lake, but it is for the cabin dwellers and they may not let you park there if you are not renting a cabin). Once there, there are trails all along the shoreline, and most people don't want to bushwack so you wont have as much competition. Sounds kind of complicated but you will find it. Used to be very good fishing there.
Beside that "secret" lake (it is really not a secret), at the main lake (where the rangers offices are) you can rent canoes, paddle boats, and the other two lakes you can rent johnboats.
I would not avoid it.
Beyond that check out the Cahaba river running through Birmingham for all manner of fishing, including largemouth and Redeyed bass.
Another place is Lake Purdy off hwy 119 in Inverness
I had to move from Birmingham to take care of family this year, but I lived there for over 20 years