Hopkinsville is a small city with a handful of decent options concentrated downtown and along the main commercial strip. Southern cooking is the default — fried chicken, catfish, country ham, biscuits with gravy. The downtown area has a few locally owned restaurants worth seeking out; most of the chain options are on the edges of town.
The Pennyroyal region is known for its agricultural produce — sweet corn, tobacco (historically), and in more recent years, small farms raising heritage breeds. Farmers' markets in season are a good source of local food. For a beer in a relaxed setting, downtown Hopkinsville has improved significantly in recent years, with a couple of taprooms that serve local craft beers alongside Kentucky bourbon.