Hi M.,
Check out the online Birthday Party Guide at www.kidwinks.com. There are hundreds of places listed (scroll to the bottom yellow area, and click on the link that says "List all Birthday Party Places") from throughout the Chicago area. If you become a member of kidwinks, which is free, you can then sort that list by distance to see what's closest to your house.
Kidwinks is a great resource for finding things to do and places to go with your kids. There's an Events Calendar and even a Kids Eat Free Calendar (click on a day to find where kids can eat free that day). If you sign up for their emails, you'll get an email each Monday morning with some hand-picked events coming up that week, including a link to all free activities, free days at the museums, and more. Again, all of these results can be sorted by distance from your house as long as you're a kidwinks member and logged in.
Here's a link to the Birthday Party Guide: http://www.kidwinks.com/ForKids/6/KidsBirthdayPartyPlaces...
Happy birthday to your daughter!
J.