Elementary School in Manhattan

Hello All

We are looking into the possibility of relocating from London (Essex)  > New York and I was wondering if there are any really good public elementary schools near Greenwich Village/Chelsea/High Line?  I have an 8 year old and would like to find a good school but don't know where to start? 

Any help appreciated.

Thanks so much!!

Public: your address determines the school. Google school district, city and county. Lots of info from parent groups and curriculum comparison.