For lunch you absolutely don't want to miss Slyman's on St. Clair. (http://www.slymans.com/) Only open 6AM-2PM, and there will be a line (especially for lunch) but by far the best corned beef sandwich anywhere I've been in the country. I have friends that travel from Chicago to get their corned beef sandwich. Oh yeah, and they're one of the ones that was on Diners, Drive-ins and Dives.
PS - Good enough for the President to eat there...