In NYC, if you want an experience with students, Columbia University does have a dental school where you can go. I don't know if they do pediatrics, but I was happy with the work I had done there.
For pediatric dentists, after a very very long search and 4 different dentists, we have found Dr. Alan Azrak in Park Slope, Brooklyn. He is wonderful and thorough and my nearly 4 year old nursling sits on my lap the whole visit and also nurses in the chair after the visit. He encouraged nightweaning, but dd was 2 1/2 and already in the process of nightweaning at the time. He does not do the oral sedation or general anesthesia, but instead gently introduced the ideas and tools to my dd, and then used the same kind of numbing shots used on adults. She sat on my lap and if we wanted a video, they were happy to play something to take her mind off the work. She's had caps on teeth that were too far gone for fillings and fillings for other teeth. FINALLY, about a year ago, she was able to go for just a regular cleaning and no more work that needed to be done.
Happy with my DH, 2 kids, dog, fish, and frogs