Try to see a show at The Metro. It's a great venue. Near Wrigley Field, in Wrigleyville, the hip part of town.
It doesn't matter who you go to see. It's even more of an adventure if you don't know the bands at all. Big acts have started out there, like Smashing Pumpkins, among others.
Then just cruise the bars in that neighborhood. You'll meet people who will tell you what's up that night in particular.
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It can be hard to get in to see a Cubs game, but few parks can compare. Mostly just walk around. Stroll through the parks. Chicago comes alive in the summer time, and people are generally friendly.
EDIT: You'll be there in October, so probably no Cubbies for you. And it could be cold. But still explore.
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For any other concerns, be sure to look at
http://chicago.craigslist.org/Start looking and posting there with questions about room and board, especially.
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One more tip. Whenever I first get to any city, I pick up a copy of their alternative weekly. Like NYC has
The Village Voice, and Chicago has
The Chicago Reader. Consult that resource for entertainment listings and tips on where to eat, where to chill, where to see and be seen.
Enjoy!