Moved to the Chicago suburbs 5 years ago from the Bay Area. Have spent a good amount of time in the city. I agree about this city being underrated. Some things I enjoy in Chicago:

Walking the 606 - similar to the highline in NYC
Piece Pizza - New Haven style, one of my favorites in the city
Pizzeria portofino - mussels and pizza sitting next to the river, river walk before or after
Lincoln Park Zoo - really pretty place to walk around and free
Trivoli Tavern - Down a cobblestone alley, speakeasy type vibe. Love the bone marrow pot pie and pasta ala vodka. I hear the burger is also very good.
Twin Anchors - classic chicago vibe, comfort food. I suggest the ribs.