Hi J.. Welcome! We like Pedios on Chicago Ave. The main doctor my kids see is Dr. Claus, but all of the doctors in the practice are good. They have decent hours, and morning call hours when you can talk to a nurse. I've never had to wait long. I believe they either don't take HMOs or only take BCBS HMO. I believe they're affiliated with all the major hospitals including Children's in Lincoln Park as well as Rush and Loyola, but you might want to ask about that if it's important to you.
When we first moved here we went to Ad-Park Pediatrics, which I really can't recommend - long, long waits and they don't open until late in the morning. In all of my experiences with them, they didn't seem very patient-oriented at all.