Al, the Pinhoti is a great trail running all through the Talladega. Lots of access points, varied terrain, good water. You can get trail guides here: http://www.pinhotitrailalliance.org/sitemap.html. There are several lakes on the Pinhoti where there is good bass/brim fishing.
Then of course there's the Sipsey Wilderness in northwest Alabama: http://www.sipseywilderness.org. The Sipsey River runs small though and I'm not sure how many fish are in it.
The Little River Canyon doesn't have any long trails to speak of, but there is camping and river fishing.
There's no fishing on it, but I'd also recommend the Pine Mountain Trail in nearby Georgia: http://www.pinemountaintrail.org.