Troll Pub has always been my favorite in that part of town, under the 2nd Street Bridge, right next to the YUM Center. Good fish and chips!
Just across the river from the YUM Center is Rocky's on the River, awesome calzones, pizza, and lasagna. Has one of the best views of the city of Lousiville on the patio dining area. Papa John's first job was working for Rocky's. You can walk to it from the YUM Center, did that a few times, but if you eat to much at Rocky's you'll wish you had drove.
All the suggestions so far are good ones.