I haven't sampled the night life in Chicago myself but am reliably told that all of the many Chicago districts offer night time entertainment. There are apparently over 380 bars and clubs alone! You might be best trying the blues club, Blue Chicago first. This is said to have great mood as well as great music. If you're older and not too adventurous, then Kingston Mines is a safe choice if not wildly exciting. Winters Jazz Club is good if you're more selective: excellent music I'm told as well as craft cocktails.
For something really different and memorable try an evening of magic. Chicago Magic Lounge offers a full evening's entertainment with magicians performing card tricks at the bar or table, a library of magic materials, secret doors and an amazing intimate art-deco style theater with offering music, magic and more. If I was a tourist in Chicago, I'd make my best night here.