If you find a pediatrician you are interested in, see if they do new patient conferences.
The practice I work for does this. For us it is at the end of the day. One of the docs takes time to meet with the potential patients parents, or the expecting parents. They give them a tour of the office and talk to them about how the practice is run. They also answer any questions that they may have.
The meeting doesn't take long, 15-20 minutes or so, depending on how many questions they have. It's gives them a good feel of how we work, and if it would be a good relationship.