It is true that we cannot comment on schools, or recommend one. Beyond that, what you consider a good public school may not be what someone else considers a good school. It is very subjective. Perhaps one parent cares about math and science; another about the arts; another about the physical facility, another about sports teams, etc. I would suggest you go to the NYC DOE site and put in some addresses in the neighborhood. It will tell you what school the address is zoned for. Then you can read more about that school. Then you can go to a parent site to see what parents say. The DOE site is: http://schools.nyc.gov/default.htm. I like http://insideschools.org/ which many of my buyers have found useful.
If you are moving into NYC, you must test to get into a school from middle school on. Another layer of challenges that lie ahead. If you choose private, you will have private school exams to take and for public, another set.