Obviously, everyone will have their own opinion on this...here's mine. Feel free to disagree or offer a different point of view. This is based on interviews and opinions I heard along the way. Please keep in mind that I have a certain degree of bias as I'm currently an intern at Montefiore.
1) Columbia - defnitely the top program in NY, one of the best in the country. Negatives are that it is supposedly malignant (although you'll hear varying opinions on this) and has a very rigorous schedule. But academics are excellent and fellowship placement is awesome.
2) Montefiore - again, I'm biased, but I think the program is a combination of strong academics, awesome facilities, and great camraderie. The residents here are from excellent med schools, but the atmosphere is not malignant at all. Everyone is very laid back and always willing to help each other out. The downsides include a lot of q4 (if you prefer night float..but we do get out at 9:30 am post-call) and a high pt. volume. The hospital is extremely busy...but this means you get to see a great volume of general peds in addition to all the subspecialty & surgical cases. You dont always mind working so hard because everyone is easy to work with (and we have a pretty good guy/girl ratio so it's a nice balance of personalities.) We also get great "perks" (great pay, free food 7 days a week, super cheap housing 10-12 miles from manhattan, great health insurance). Overall I think it's a great combination of academics and a pleasant work environment, but it's definitely on the rigorous side (it gets better during 2nd & 3rd yr).
3) Mt. Sinai - I also really liked this program, and think it's on the same level as Monte, behind Columbia. The positives are a great location, a relatively "cush" schedule with more manageable pt. volume, a strong departmental reputation, and excellent fellowship placement. The downsides are the facilities (older, and not a true stand alone peds hospital) and the heavy volume of GI/liver patients (unless you are dead set on going into GI)...some former Sinai students said they thought there was not nearly enough pt. variety.
4) NYU - another very strong program. Excellent academics, and very nice facilities. Most residents seemed fairly happy. Downsides were an odd call schedule, in my opinion (1 week night float every month), late days (signing out at 6-7 pm every day), and a somewhat strange dichotomy between Tisch & Bellevue. But it's in a great part of the city, and overall it's a very good program.
5) Cornell - another program in a great location, with awesome affordable housing. The dept has a solid reputation, but I was a little disappointed during my interview. I've heard that residents don't see a great deal of general peds, and that its not as strong academically because of the low pt. volume. I hear you do a lot of surgical months at HSS, which may not be that beneficial for your career as a pediatrician or subspecialist. The facilities are OK, but its just one large peds floor and not a children's hospital. But they do have excellent fellowship placement.
6) West Chester/NY Med - this program may not be well known, but I think it's up and coming. The facilities were by far the nicest I saw anywhere, and I think they have very solid academics as well as a pleasant environment. Excellent pt variety. Everyone seemed very happy and the faculty seemed very interested in teaching. The downsides are the location (if you want to live in/near the city, but if you're looking for a suburban life, this might be perfect). And it's still under 1 hr from Manhattan.
7) Jacobi - this is a solid program, especially for general peds. The facilities were nice (they just built a new hospital) but again, it's not a children's hospital (if that matters to you). I think you work hard but you're not overworked. I think the downside is the lack of access to subspecialties. I think their fellowship placement was OK. Overall a solid program.
8) North Shore/LIJ - also a solid program, with good academics and nice facilities. Downsides were the size (40+ residents/year) and few call-free months. Some residents seemed unhappy on the interview day. But friends who are there now don't have too many complaints. I think they also have solid fellowship placement.
Hope this helps...feel free to disagree. Everyone always says this, but it's true that ultimately, you have to go where you feel most comfortable...you can't get caught up with rankings or reputations. There are many solid programs in NY and you would do well to match at any of them. Good luck!