The place by the stock yards is Golden Ox. Gates is very good, some people like Arthur Bryant's, but it's not my favorite. If you want Arthur Bryant's, go during the daytime or go to Ameristar Casino. There's one there too. The Bryant's downtown is in a section of town you do not want to be in after dark. You'd need two mean dogs and a 45.
Hereford House is good, as is Plaza III and Majestic SteakHouse, I've been told. I don't think any of them are close to cheap though.
Another good place to eat is Stroud's, famous for their fried chicken with home style cooking and it's reasonable.