there are shops, but i don't think they're worth visiting on a trip with limited time. imho there are cooler things to do in the city.
i say this because i just don't think there is much of a chicago tea scene, and the tea likely won't be as good as what you've been buying online (as someone making a strong effort to get the best tea you can possibly find). imo it's like this in most of the US with a couple of exceptions. i know there's a couple of shops in NYC that have
good tea (of course with commensurate brick & mortar + NYC markup). same in cali. but i'm not aware of shops like that here.
we seem to only have shops that push this kind of thing:
they might have some normal teas too, but nothing worth making a trip out of.
i'll share a few though and let you decide
https://www.teegschwendner.de/en -- legit, respected german tea biz, but again, the tea is not as good as what i think you're accustomed to drinking. i liked going here when i was starting out.
https://easthilltea.com/ -- relatively new, this is the only gongfu-aware biz i know of. problem is there's not enough of a tea scene here to justify stocking super good tea. i had a few teas here with friends, but they were just like bulk oolong. also, it was an odd experience. they have a higher end section of the menu, and we wanted to order one tea at a time from there and share. however, we were told those are reserved for special appointments with the 'tea master' (who was not in at the time), and we could not brew them ourselves because we wouldn't know how
also, we couldn't just do one at a time and share because that's not how it worked. they insisted on giving each of us our own bamboo tea tray place setting with teapot and tea pet (which they wouldn't let me remove from the tray), and the server buzzed around us with 4 beeping kitchen timers clipped to her apron trying to micromanage everyone's experience. i still want to go back there and try again though with that said. i think it's awesome that there's a gongfu tea house in chicago.
https://todd-holland.com/ -- nice little shop. if the owner Bill Todd is there, he'll talk your ear off. nice guy with some cool stories. they have some decent teas but again not worth the trip just for the tea if you're already making an effort to buy the best tea you can find online.
https://tealula.com/ -- i'm not personally into flavored teas really, and that seems to be their focus