Richard beat me to it...
I agree with the Ramsi's recommendation. You won't be able to walk it, but they are (in my opinion) the best option for such a late dinner, and you'd have an opportunity to see the Highlands (Louisville's beatnik neighborhood). Probably a 6 or 7 dollar cab ride from your hotel. They're open until 1am on the weekdays and 2am on the weekends. Really impressive that they can keep up the business so late but I think it works because they are the only ones that do. It's not fine dining, but I strongly recommend a look at the menu.
http://www.ramsiscafe.com/