I'm thinking the game time period for Fallout 4 should be from 2066 to 2088, the start of the invasion and after the bombs fell. The player could be living during that period, maybe his/her family can't afford a spot in one of the Vaults and had to hide in a bomb shelter under the house.
I dunno, what ya think?
:ps: I like that idea about the brotherhoods in the westcoast.