Krome Sports Bar:
http://www.kromebilliards.net/Home_Page.html (heard it's pretty good)
Fox and Hound: 2800 Lakewood Village Dr.
North Little Rock, AR 72116
Phone: (501)-753-8300
(played there once. Nice place. Good looking tables, but they rolled funny. Possibly been releveled since then.)
Rack 'Um Pool Hall: 2817 Cantrell Rd Little Rock,Ar 72202
Phone: (501)-603-0066
(no clue)
Midtown Billiards: 1316 Main St, Little Rock, AR
Phone: (501) 372-9990
(No clue. Never heard of it. Just found it on-line.)
There are probably more, but a Yahoo or Google search might find something for you.
I'm 2 1/2 hours away. If I was going to visit my brother in Conway, we'd hit some balls, but I don't have any plans to get down there right now.
Good luck and please give us a review of where you went.