There are all sorts of good local places in Lexington. It all depends on what type of food you want.
If you want a higher end steak and food then I recommend Malones.
https://bluegrasshospitality.com/malones/ They have multiple locations and other restaurants in the same building that you can order from if you want.
A really good casual place is Drakes. It caters to a younger crowd, has sports bar area with walls they can open during the warmer days.
https://drakescomeplay.com/lexington/
A restaurant that loves beer and a bar that loves food. Over 20 craft beers on tap, big burgers and the freshest sushi in town. Your go-to for lunch, dinner and late-night, Drake's is a free-wheeling, fun-loving kind of joint. A place to hang out and let your hair down. A place to let yourself go a little. Come play!
As already mentioned Ramsey's, Joe Bolognas, and Winchell's are all solid choices as well.