Mine would be you start in the middle of a new war. Not a war with another country, but between two (or more) major factions trying to take control of what's left of the U.S. We've seen and heard of the Enclave and the Commonwealth. Perhaps fast forward 25-30 years into the future and the Enclave has rebounded in the West and is trying again to reclaim the East, where the Commonwealth has begun to spread out. The two have massive armies and are focused on their overall objective -- retaking the U.S. Neither wants to budge, and so a war ensues. You begin as a neutral party, and can remain so throughout the game, or side with one side or the other (or insert one or two other factions).
The possibilities are endless...