My Precinct

[Alcon]

http://gis.co.suffolk.ny.us/vim.htm

I have never seen a state-wide precinct map for any state (although I've seen one for the District of Columbia).  I imagine it is not easy to find, especially detailed - there are a *lot* of precincts in New Jersey.

[Alcon]

Most major counties have their own precinct maps.

For the most part, although some counties use look-ups instead.  Annoyingly, many of these do look-ups based only on registration (that is, if you want to find out what precinct an area is in, you have to know someone registered right there).  Some of them have address-based looks ups, and some states centralise their databases.