The Lincoln Square place was the Brauhaus which closed a couple years ago (sadly), although Lincoln Square still has a great Maifest and Oktoberfest and the Dankhaus German cultural center. There is a smaller place called Himmel's that by quirk of history has both German and Italian food, it's a bit like sitting in someone's rec room (in a good way.) The only original beerhall place these days is the Berghoff downtown. We lost Zum Deutchen Eck, the Golden Ox, Math Iglers, and many more over the years, there are a few in the suburbs. Chicago has like 70 breweries so there are many great choices:
-For German try Dovetail, both head brewers trained in Germany and many of their malts are brought in from Germany (the rauchbier malt comes from Bamburg as it should!) great taproom as well, they also do sours - there are a couple other good ones right by here (see the link below)
-Alarmist on the northside is great, do lagers and IPA plus some Czech-style beers, would be a place to stop on the way to or from the airport given the location
-Is/Was just opened a taproom near me, they brew a million different versions of saisons, all excellent, the beer list is like a phonebook as they often will only make one batch and the move onto something else - worth checking out what they have, pretty unique
https://www.iswasbrewing.com/buy-beer
-Not chicago but nearby in Indiana is Three Floyds, considered one of the best breweries anywhere (and has one of the best beer festivals anywhere, Dark Lord Day, which draws people from all over the country and elsewhere) - their beers are widely carried here
You can make a good trip up and down Ravenswood:
https://chicago.eater.com/maps/malt-row-breweries-ravenswood-beer-taproom
-I live right near hopleaf and have been going there for 25 years - the food, atmosphere and beer list are great with several Belgian brewers providing special brews just for them - they also carry a number of domestic microbrews
-If you can find it while you are here one of the best and most unique breweries is Scratch (I think now only carried at Beer Temple) - it's a tiny artisan brewery from downstate Illinois on the edge of a national forest - natural sour style and they tend to use other bittering agents than hops (wild carrot, marigold, etc.) - they are fantastic - James Beard (top US food awards) award winning
I can go on!