I grew up in Berea, and worked at Boone Tavern for a few years in high school before moving here for culinary school...
The cafe Eliza mentions is Papaleno's, which has a nice bill of fare by way of pizza, subs, salads, etc. It sits on the opposite side of college square.
Wan Pen is an interesting little asian spot (just off I-75, exit 76... near the walmart) The owners are Thai,
and although it's a bit like any other americanized asian restaurant in a any town, the thai dishes are pretty tasty, and there's plenty of stuff kids would love.
Rio Grande Mexican, nothing more than tex-mex... but never ever had a bad meal here.
Dinner Bell Restaurant, think cracker barrel... but independently owned.
Mario's Pizza is always good for a sit down pizza place.
and the aforementioned Boone Tavern is always a solid option,
and between there and Papaleno's is Berea Coffee & Tea Co. (which Eliza mentioned... also in college square.)
Berea, KY Official Website - Area Dining
hope any of this helped!