I asked this question back in August, when I was planning my daughter's first birthday party. The link to my question is here: http://www.mamasource.com/request/15065349856908279809
We ended up having an ice cream party at Bobtail Ice Cream Shop on Southport. It was perfect - better than I had ever imagined. They charged $100 for the party space, and then $5 per person, which covered all food and beverage... our guests had ice cream, ice cream splits, milkshakes, coffee and coffee drinks, etc - all for $5 per person. They were SO nice and friendly, we just loved it and I'd suggest it again in a heartbeat.
My daughter's party was in November at the Southport location, and that location is now closed for the winter, but the Broadway location is open. I'd definitely suggest checking out Bobtail, or another ice cream shop, it was just perfect.