I can only speak to Einstein and NYU's programs, as Mt. Sinai was not accepting applications this year, but here are my thoughts on those programs as someone who is graduating from an NYC med school and rotated or interviewed at most of the programs in the city:
Einstein, despite its location in the Bronx and lack of prominent national reputation, is definitely a strong program. There's currently 7 residents and ~8 attendings, with strong clinical volume in every disease site, and especially have an abundance of brachytherapy, including H&N brachy, to which access is limited at many other programs. The residents cover 2 hospital sites in the Bronx: Montefiore hospital and the stand-alone RT facility near Weiler Hospital and Einstein Med School. Additionally, they have a 3 month rotation at Beth Israel in Manhattan, which typically involves working with Lou Harrison, who was Chairman of ASTRO last year. The most prominent faculty member at Einstein is Dr. Guha, the Vice Chair, who splits his time ~30/70 between clinic and lab and is head of RTOG Translational's GI subdivision. He has probably the most connections in the field of anyone on the faculty and will definitely go to bat for his residents. Residents spend 6-9 months on his lab/clinic service, and 3 months at a time on each of the other services. While in the past the department has had a "private" feel to it, it is definitely moving in a stronger academic direction, with regular visiting professor grand rounds from prominent faculty and all of the residents presenting abstracts at ASTRO the past 2 years. However, with the exception of the lab research, most of those projects remain resident driven. All in all, I'd say Einstein is a strong program with lots of opportunities for movitated residents, although you won't be spoon fed.
As for NYU, it is a relatively strong program, a little smaller than Einstein with 6 residents and ~5 attendings. They recently lost 3 faculty in the past year, one of who,m left for private practice and two of whom moved to other NYC departments. Peter Schiff, the former Chair at Columbia, recently joined NYU's faculty, which does balance some of the attrition, although I wasn't quite sure what to make of all of the faculty turnover. The residents there primarily cover 2 sites, Tisch Hospital and the NYU Cancer Center (2 avenues apart of 34th st), and also see consults at Bellevue, about 8 blocks south of Tisch. The Chair, Dr. Formenti, is well known in breast cancer, is supposedly is demanding of her faculty, but does not actually interact with the residents all that much. Dr. Narayana, the PD, who used to be at MSKCC and came to NYU ~3 years ago, is very actively involved in both Peds and CNS clinical research. There do seem to be some basic science/translational research opportunties through Dr. Formenti's connections at NYU, although I'm not sure whether she has her own lab. NYU's program seemed to be strong in most disease sites, and they get their fair share of brachy as well. Their program also seems to be fairly "private" as far as the attendings' commitment to academics go, with the exception of the previously mentioned attendings. The residents work hard, and definititely complain about this aspect of the program, but you'd be hard pressed to find a program where residents don't complain about something. All in all, a solid program, although I'm not sure I would say anything about it is particularly exciting or unique, other than the location of course (which is phenomenal).
As for Mt. Sinai, the PD at MSKCC told me she had a high degree of respect for their graduating residents, but a friend of mine had a very negative experience rotating there, so take that for what you will. They also have a reputation for poaching residents from other programs (not cool). That's all I know as far as that program goes...