This may be a quiet time of year in terms of homeschool specifc events, but there is still lots of fun, even educational fun, to be had.
Came across this information packed site, called Chicago Kids. There you can find details about the happenings in Millennium Park among other things.
If you are looking for activities to spice up your summer, feel free to check through their ideas of free activities as well as many that charge admission. They have a calendar that can give you dozens of ideas for any day of the week.
Also, don’t forget the Museum Adventure Pass that is around for another couple months and has some great deals.