Ok, so I've only played 3 and I need a little help here. I want to compile a list of Fallout series locations by U.S. state. Like this:
Washington, D.C.: Capital Wasteland
California: New Californian Republic
Can any Fallout vets gimme a hand?
If you really want to keep a list that's as true as possible, I'd try the Fallout Wiki if I were you. Otherwise people can argue about it forever, for instance: "Arroyo is in California!" "No, it's in Oregon!". It could go on forever. If you have any doubts when looking at the Wiki, I'm sure Ausir can help you out.
But to get you on your way:
Fallout 1:
California:
Shady Sands (NCR in Fallout 2)
Vault 15
Vault 13
Junktown
The Hub
Mariposa (Military base)
Necropolis
The Glow
The Boneyard
The Cathedral
There are some more, but I haven't played FO1 in a while.