I like to fish for rainbow trout in Mountain View (Mirror Lake at Blanchard Springs State Park). It's stocked periodically, so the action varies, but it's always fun. It's several hours from Little Rock, but you can camp there and make a fun weekend of it.
There is also some brown trout fishing at JFK Park in Heber Springs, but bring your waders. It's much closer to Little Rock, and there are also places to camp, so it's fun for the whole family.
I've never tried the White River, but it appears to hold some good trout.

It's farther still, but again, it would make a nice weekend trip.
As for bass fishing, Lake Overcup towards Morrilton is close to you, but you probably need a boat to do well. Lake Maumelle is also close to you, but again, a boat helps. Never fished Lake Conway, but it's definitely an option. As for how good the fishing is now, I wouldn't know..it's been a few years since I've fished in central AR. Hope someone in the know can fill you in on this soon.

This site might help:
Arkansas Fishing Report: Lake Conway