For the family? Not much really. Some of the local, small, not-for-profits might have a children's show on the weekend that might involve puppets, but there's nothing that stands out puppetwise.
"Avenue Q" is going to be in town around then. But that really isn't family friendly (or maybe it is. I don't know your family).
And there is a bad puppet improv show called "Felt" that runs on Wednesday nights. For an improv puppet show, it isn't very good at either. If you go, make sure there isn't a Cubs game the same night. The theatre is right around the corner from Wrigley Field.