LucyLastic, as you are probably aware, things are organized a bit differently on this side of the pond, and in case you are unfamiliar with the local geography:
What people refer to colloquially as "towns" are actually villages and hamlets, which are within actual towns; and, because villages and hamlets are referred to as "towns", then, many times, the error is compounded when actual towns are referred to as "townships".
Also, many colloquially refer to a "downtown business district" in a hamlet as a "village".
NYS Geographic Glossary and
Excellent Long Island Geographic Resource may be of some help to you in understanding the geography of "Lawn Guyland".
On LI, You Ain't Where You Think You Are, rev. 1 may help you understand the great geographic confusions caused by non-conforming ZIP Code postal zones.
When you do find a house that you like, you can find out in which community (city, village or CDP) that house is actually located, which is oftentimes different from the community named in that house's mailing address, by using the Census Bureau's
online address search function. (CDP or
Census
Designated
Place is the Census Bureau equivalent for a hamlet in Nassau and Suffolk Counties.)
And, very importantly, among other things, the Census Bureau's
online address search function also indicates in which school district an address is located.