There are several very nice little cafes at the main market Ovoshnoi Rynok. They are not expensive, and are cleaner and serve fresher food than many in other areas. They have quite a good selection of food and it is well prepared. Best though to only eat HOT food, for safety's sake.
Try shopping in the many markets for local produce. There are great bargains to be had on meat and vegetables. You might have to overlook some of the health standards, but as long as you wash and cook the food well - you should not have a problem.
