Rather than a list of what "areas" are not cities, villages nor hamlets, here's some information on the actual cities, villages and hamlets:
There are 2 cities and 13 towns (as well as 2 Indian reservations) in the bi-counties and the 13 towns (3 in Nassau and 10 in Suffolk) are further sub-divided into 96 villages (incorporated municipalities) and 195 hamlets (unincorporated areas), yielding 293 communities (2 + 96 + 195 = 293).
..............Nassau......Suffolk........Total
....cities............2..........0..............2
...villages.........64.........32.............96
.hamlets..........70........125............195
.....total.........136........157............293
For a good set of town-by-town maps showing all the villages and hamlets in each of LI's 13 towns (3 in Nassau County and 10 in Suffolk County):
Excellent Long Island Geographic Resource