The St. Charles Wendy's is actually really good, and very accessible to the Dome (good soda machine selection, too). That's probably my favorite. White Castle is pretty good. Haven't had Carl Jrs., but have also heard good things. Oh and McDonalds Big Mac is pretty incredible.
In Midcity, Brown Butter makes a terrible burger in the thicker style, if that's your thing. Harrison Ave in Lakeview actually has several good burgers...if you have NO taste.