There are a number of sites that show information on local schools. They often have links to real estate sites that show properties in the area.
insideschools.org is above all my favorite. It is a local non profit run by Advocates for Children. It has a tremendous reach and depth and the first thing any parent worried about schools should do is sign up for their newsletter alerts and send them a little tax deductible thank you for the incredibly good work that they do. (I am not affiliated with them, I just love them.) You can "Ask Judy" a question, browse their forum, check their calendar, and most importantly read their reviews. The data at the beginning of the review (test scores and numbers) are updated every year and any change in principal or location is added right away. Because they review every school in the city, some reviews are a couple years old, check the dates at the end of the review. Remember that all parents that comment on schools are on a mission. They either love the school or hate it and it is difficult to get an objective reading of how much the parent body as a whole feels. If you have trouble searching for the school by name, also try searching by zip and age level, one of these two ways always gets results.
schools.nyc.gov is the Dept. of Education's website. There are individual school pages here (go to find a school). You can find copies of state and city reports on each school under the "statistics" tab on their school page. I recommend browsing the menu on the homepage, often publications, calendars and procedures are listed here or downloadable as pdf files. This is a very large deep and sometimes confusing website. If you find a page that you like, bookmark it so that you can find it again.
charterschoolsearch.com is a searchable national database of charter schools
nycprivateschoolsblog.com is a terrific local blog that is chocked full of information including listings of over 800 private schools in the city. This blog is making a real attempt to cover all boroughs which is refreshing.
greatschools.org is a national site where you can search by city, or address, district etc. The search tool is clumsey at best and it is difficult to browse. The comparison of local schools also gives a weirdly haphazard and incomplete mix and sometimes elementary, middle and high schools are incorporated in the same list. For a national site that doesn't really address the complexities of the NYC school system, it is the best by far. They give a number ranking to the schools that is mostly based on test scores which can be misleading and are only a small indication of school's quality. There are parent comments and lots of general articles.
schooldigger.com searches by zip or address or city and gives a clear map of public elementary choices, but their ranking system is out of date and based on scores. They have very clear links to real estate if you are looking for that.
schoolsk-12.com Their security certificate expired in 2008 so I haven't downloaded a "premium report" from them, but from their sample there is nothing on the report that isn't located on the statistics page of the DOE school's homepage.
All the others are just lists of addresses.