FYI, less than 5% of Chicago's current rail system is underground, so they really don't have much of a subway, especially where you guys are presently located (in a suburb). Public transportation is mainly by bus or the "L," which is slang for the Elevated Rapid Transit train. However, since this is an alternate reality, we can just assume that a fairly recent underground transit line has been constructed in the Orland Park area.
Voda Vosa, I am assuming in your post that when you said you were headed for the market you mean the mall on the northeast corner, since much of the smaller shopping center to the west would be in various states of ruin.
Also, I don't recall seeing some of your equipment in your original write-up. Maybe it was and I just glossed over it. In any case, it would be rather odd for your character to be carrying around some of those things, although I have no problem with you having them back at the hotel (even though it seems a little neurotic to bring a gas mask with you to an academic congress, which seems to be your character's reason for being in Chicago). The sword cane, crossbow, and 10 bolts you can carry on you, as well as some form of identification. The crossbow is partially disassembled in a case with the bolts. You can reassemble it at a moment's notice in 1d4 rounds. Everything else is back at your hotel room, wherever that is; you decide.