Neonatologists love to have students follow them on rounds or night call. The best thing is to try to follow the same doctor over a period of once or twice a week for a month or so to learn what happens to the babies you've been seeing. As far as finding one, the simplest way is to call the hospital, ask for the neonatal ICU and then ask to talk to one of the neonatologist. Do this in the afternoon so they aren't on rounds.
If this seems too "forward" (believe me, they'll like it, not be upset), you could call up a pediatrician in town if you know one and they usually know the neonatologists and could help you.
If that is still too much to try (really, trust me, no one will mind...), then you could send a letter addressed to the "chief of neonatology" at the hospitals you are interested in and describe your interests, etc.
"oldbear" professor