There is a dearth of Jewish Delis, authentic or otherwise, in the Chicago area right now. The best, and most obvious choice, based on your desire to stay close Michigan Avenue, is Manny's Deli
. You can read the Roadfood review here
Another option is a place this lifelong Chicagoan just recently heard about, but apparently has been around since the late '30s. Frances' Deli
on the near north side is a short cab ride from Michigan Avenue. It appears to be a more varied and somewhat trendy menu than Manny's. But if you want full table service and a cocktail to go along with your Corned Beef Sandwich, Frances' is the place. Roadfood review can be seen here
It's not that we're short on Delis, mind you, it's just that other ethnic groups seem to have overrun that market. Italian, Polish, and German Delis are in abundance. Jewish Delis, which could once be found in all quarters of the city and suburbs are fading away.
Have a great trip!