Manhattan

The center of activity with the most places to visit. Great for beginners.
Major Areas: Central
Vaults in this area: 2

Brooklyn

A large area, but mainly barren.
Major Areas: The Octagon, New Calvary Cemetery, Queensboro Bridge
Vaults in this area: 31

The Bronx

Many major factions have HQs in this area.
Major Areas: Akeestam, Trade Runners HQ, Belmont, Fordham University, Bronx Zoo, Deathclaw Camp
Vaults in this area:

Queens

tba

Staten Island

tba. lots of super mutants here

Rikers Island/Vault 58

A decent sized island in the middle of East River. It used to house a correctional facility, but it's also home to a Vault, which contains a large population of androids.