I grew up in the St. Louis and also have a weakness for White Castle burgers. I remember when they were $0.12 each! But as a kid, my favorite was Steak 'n Shake. Whenever I get back to the midwest I have to grab a few steakburgers. They are working their way eastward, and have a location in Paramus opening soon. My daughter just told me they have a location in downtown Manhattan now (she also became addicted while in college in St Louis).
http://www.steaknshake.com/
http://www.steaknshake.com/