There is a restaurant in the Doubletree Hotel, in the same building. The Marriott is down the street. Downtown on a Saturday most of the quick lunchtime places are closed but there is a lot of activity down around the River Market and the Clinton Library. There is a Bruno's red sauce Italian on Main that is a nice sit down place. Natchez, South On Main, The Capital Hotel Bar, the Flying Fish, the Root Cafe, Boulevard Bread are all worth a visit, as is Whole Hog Cafe which is just a short drive.
Welcome to Little Rock. You are in for a treat.