C.C.
I too have a three year old daughter and have encountered the same problem. My husband and I considered a Lutheran school near us, but the cost was too high given what they seemed to be offering. What I have opted to do is place her in several activities through the park district and Wright College. She did a "Skills for Reading Readiness" in the spring which ranges from age 2 to 5. I intend to put her in again this fall. I am also adding on a math and possibly science class. She knows most of the stuff, but it is great for socializing, gets her ready for the transition to structured schooling next year, and they always end with an arts and craft project that she enjoys. All of the above programs are only one day for only an hour a week, but it's something and not too overwhelming.
FYI, registration for the Chicago Park District begins August 14th. If you choose this route, take it from a mom who missed out on everything for the summer, be ready to register on August 14th. They will be filled shortly thereafter.
Good luck with everything.
C.