St. Peter’s, 110 W. Madison, is the main place for confessions and Catholic ministry in the Loop. Long has been. The Franciscans have a special devotion to this sacrament.
Another public chapel in the area would include the Daughters of St. Paul bookstore (but it is small and wouldn’t likely be offering confessions to the public).
Holy Name Cathedral, obviously, North Michigan Ave. area. (Chicago & State, actually - like you don’t know where THAT is.)
Old St. Mary’s used to be in the Loop but has moved to serve the newly burgeoning “South Loop” area, and is located on Michigan and 15th, roughly.
Assumption Parish, 323 W. Illinois, is hidden in the shadows behind the Merchandise Mart. They might offer confessions prior to their noontime weekday Mass.
Catholic Charities (near the cathedral) has a chapel which is open to the public, at least at times, complete with adoration certain days.
Old St. Pat’s in what is now called “West Loop” near the train stations. Don’t know what their confession schedule is like, however.
Off the top of my head, those are the main spots downtown.