First, I would ask your OBGYN for a recommendation on a pediatrician. Also, the maternity ward or birthing center you are delivering at will very likely have a pediatrician that they use (if you don't already have one), so you can call and get suggestions from them.
My OBGYN suggested a pediatrician, and he happens to be in the same practice that a good friend uses for her daughter. All I did was call, let the receptionist know that I was pregnant and when my due date was, and told her my OBGYN had made the recommendation. I asked to make an appointment to speak to the doctor, and had no problem doing so. I have a 5pm appointment (so I guess he's meeting with me after business hours). I don't see why other pediatricians would have something against meeting with prospective parents, as they will be called to the hospital very soon after delivery to check on the baby .