Luckenbooth's in Black Earth. Go to the shoe store, shop if you need to, and continue south into "downtown." It's on a corner on your right.
Fantastic food, real baked goods. Lots of locals. A Scottish hostess who loves to tell jokes that are hard for Meerkins to understand.
You can't go wrong here. Just don't be in a big hurry to get in and out, and you'll have fun.
Another option, a few miles farther from Madison, is the Old Feed Mill in Mazomanie, which includes a gift shop.
Since you're a baseball fan, if you want a sports bar experience, stop at Rookie's at the corner of 78 and 14. Have at least a beer here, and marvel at the stuff on the walls and the ball field.