I agree that you want a place that see's kids on nearly every shift. In the real world those 1 month olds with a fever are mixed in with all the rest of the patients. Children's hospitals are great, but ideally you train somewhere where you have to see the patient, do the workup, and make decisions before calling the Peds. team. Most of us don't work at places without Children's hospitals, so any training you can get as a resident where you are having to do things on your own, and make decisions on your own, is going to help you in the long run.
Don't get hung up on big name Peds places...good luck getting your hands on a crashing 6 month old at any of the "major pediatric centers." You'll be 8th in line behind all the specialists, fellows, and senior peds folks.
I trained at a community/academic program, all my sick pedi kids were managed by me, with an ED attending in the room, no fellows, no other residents...I wouldn't trade that training for anything.