S.
I will recommend:
All Saints Episcopal Church
4550 N. Hermitage
Chicago, IL 60640
###-###-####
____@____.com
It is not non-denominational, but it is very welcoming and inclusive, and it is very easy to baptise your child there. My husband was also raised Catholic and I was raised Baptist, and neither of us were practising. We were married in a civil ceremony. We find the service there to be a great fit of traditions that both of us are familiar with, yet it is also quite contemporary. We baptised our daughter there at 8.5 mos. In fact, they baptise people of any age, it is pretty interesting and as I said, very inclusive.
Good luck in your decision!
S.