For Fine Dining - Ashley's at the Capital Hotel (downtown) is the best in town. It probably has the most creative menu and best food, the chef is a semifinalist for a James Beard Award. 3 course meal for $49 is a great deal (especially depending on where you live), plus you can do wine pairing for additional $20 (and no small pours either). It is a fusion of french and american southern.
On a little lesser level but also good are Capeo (across the river in downtown North Little Rock) and Ferneau's in Hillcrest.
If you are in West Little Rock, Ya Ya's Euro Bistro (it is a chain in about 6 cities), it is very good and seems to be pretty consistent as to quality.
For a little more local flavor - Whole Hog BBQ (many locations but original is on Cantrell Road), has won many awards.
Flying Fish, Great Catfish in Downtown,
ZaZa's pizza and Salad is a good place for lunch or a more casual dinner in the Heights.
Cothams is downtown and famous for their burgers and southern specialties (i have not been in a while as the service was kind of slow for lunch)
Does Eat Place - Downtown, not upscale (not the best neighborhood), huge steaks, i think they are kind of hit and miss sometimes when they are cooked, but the soaked salad and the tamales are great (but it is a pretty well known institution, the original is in Greenwood, MS, but i think this was the second).
I really dont recommend any steak places (even Doe's is hit and miss, but it is local fare) in Little Rock, to much mediocre food.
Hope this helps.