I live right in downtown, and here are three locations I've shot:
-Millennium Park Garage
- A cool urban setting, I shot this from dusk to night. Careful though, there's security guards inside the garage that you'll have to dodge after a certain point :P Not to mention dodging the cars themselves... It has some pretty cool ambient lighting, though, and there's usually graffiti on the walls. Not sure if there's an office there where you can ask to shoot, but considering the School of the Art Institute is right next door (my school, lol), they're probably used to having to chase out photography students anyway.
-Fourth Presbyterian Church
- Located on the Magnificent Mile, just a little ways away from another nice bit of architecture, the Water Towers. One of the most gorgeous churches I've ever been in. Shot this in the dead of December, in a snowstorm. I asked permission from the church office before shooting, which I would highly recommend. There are almost always some people in the church (usually homeless) so I was as quiet as possible when photographing and tried to keep us off to the sides where we wouldn't disturb anyone. Obviously, this would make it rather difficult to set up any equipment there, at least inside. Outside you might be able to have someone holding up equipment, maybe.
-The Art Institute of Chicago Modern Wing (connector bridge)
- My school, so I didn't really have to ask permission
This location in specific is the elevator/escalator to the skybridge that connects the AIC to Millennium Park, and it has this cool clean, white futuristic feel that the entire Modern Wing has. Also, you'll get a lot less weird looks here, since it's SAIC (man, no one can tell me my cosplay is weird when you've seen some of the shit at that school that I have...) Fair warning: You'll be dodging groups of visitors and occassionally the Board of Directors (their meeting room is connected to this structure on the third floor), and you can't go too late or it'll be closed (check museum times on the AIC website), but other than that you should be fine.
I'll add more as I find them.
Millennium Park can be really nice to shoot in for the gardens and fountains, you just want to stay away from the touristy areas of it like the Bean (Cloudgate) and the skating rink/LCD screen fountains. I use it a lot because it's convenient for me since my school is right there. Also of interest for photographers, just about 5 blocks or so down Michigan going South you'll find the Roosevelt University's Museum of Contemporary Photography.