Other potential fight locations:
Maxwell Street Market - happens every Sunday on Canal Street at the intersection with Roosevelt (yep, it's no longer on Maxwell Street), right next to the White Palace Diner (a Chicago institution since 1939 - great greasy food. Mmmmm). It's a huge bazaar where tons of people show up (individuals, not retailers) and hock their wares. It's got everything: auto parts, electronics equipment, porn, musical instruments, food, tools, books, gardening equipment, clothing, toys, media of all kinds, bicycles, trinkets, containers, and so on. There's no rhyme or reason to where each stand is. They just set up, and it's off and running. The whole section of street, about four blocks, is closed off (except vehicle traffic can move along Roosevelt). Bands play. Thousands of people stroll through, buying, selling, and. It's quite the outdoor market. I once heard someone describe it as "the place to go to buy your stolen bike back."
Millenium Park - recently completed, with lots of cool architectural features, promenades, collonades, a concert stage, a giant reflective chrome bubble (
www.milleniumpark.org), and more. Lots of people, could be a very dynamic setting.
McCormick Place - gigantic (seriously) convention and events center. Lots of interior space with auditoriums, open floors, etc.
http://www.mccormickplace.com/
Soldier Field - home of the Chicago Bears, and a great stadium to catch a game.
http://www.soldierfield.net/default.aspx
Wrigley Field - the friendly confines (boooo! Sorry, White Sox fan here).
http://www.ballparks.com/baseball/national/wrigle.htm
Comiskey Park - also known as U.S. Cellular Field and home to the South Side Hitmen of the Chicago White Sox. Go Sox!

Go to
http://chicago.whitesox.mlb.com and check for information on the ballpark.
The Museum Campus - includes the aforementioned Field Museum, as well as the Shedd Aquarium, and the Adler Planetarium. Also just a really gorgeous area of lakefront property and harbor.
Fermi Lab - the national particle accelerator lab due west of the great city of Chicago. Way, way cool. Only thing is, it's way out of town, so not actually in the city.
http://www.fnal.gov/
Downtown Chicago itself is quite the architectural wonder, with all sorts of beautiful buildings, skyscrapers, and great locations and history.
Navy Pier - total tourist trap, but it does have a cool IMAX theater. Tons of people there (less so in the winter), could make for a dynamic battleground.
www.navypier.com
The Harold Washington Library - south loop area, and a giant archive.
http://www.chipublib.org/001hwlc/001hwlc.html
Precinct 1 Police Station is down at the corner of State St. and 18th.
Belmont Avenue in the Lakefront area is great people watching: lots of punks, goths, and other too-cool-for-cool folks. The Gold Coast is a very wealthy area of the city. Chinatown and Greektown are both cool locations. Food staples in the city include pizza (the world's best pizza comes from Chicago. No, really. It's proven scientific fact), polish sausages, hot dogs, and beer.
If you want some good brand names to throw at the players to help increase the verisimilitude (such as it is), use names like Goose Island Beer (local brewery), Frango Mints (from Macy's neé Marshall Fields' Department Store, and very popular around December), Gino's East Pizza, Giordano's Pizza,
The Chicago Tribune and
The Chicago Sun Times are the two major newspapers, Gene & Georgetti is a famous steakhouse where Sinatra used to eat when he was in town, the Rock 'n' Roll McDonalds in River North, Abbott Pharmaceutical Labs, Allstate Insurance, Walgreen's, the John Hancock building, the Aon Center, the IBM building, the Tribune Tower, the University of Chicago, Northwestern University, and the University of Illinois Chicago, to name a few.
Winter behavior: contrary to popular image, it doesn't snow all that much in Chicago (not like, say Buffalo, NY, or Maine). Sure, there's snow, but it's not always a winter wonderland. However, when it does snow, local residents dig their cars out from street parking spots, place a suitable "holder" in the newly dug spot (lawn furniture works well, broken vacuum cleaners are also good, etc.) and drive to work. Anyone who takes someone's hard-won freshly-dug spot, in clear violation of the place holder, is taking their life into their own hands.
Anyway, there's lots of stuff.
Good luck with the game!
Warrior Poet