Pacific Northwest.
It would be the major staging area for the war with China which would mean plenty of crazy pre-war tech left around, maybe something naval like some super ships left pier side at Bremerton, would explore Canada's annexation and hostility remaining between British Columbians and Washingtonians.
Add in the remnant of the West Coast Enclave left behind relocating there and them having a more forward looking view of carving out their own state mixed with a more pragmatic eye now that the Old Guard is off in DC or dead. Local powers vying for power, maybe a Vancouver Island Republic to be a political enemy and possibly reveal that an American-Chinese state emerged from WWIII in Alaska after all the soldiers left dumped there during the nuclear exchange suddenly found the need to unite to survive than keep fighting each other... and maybe they want to expand south and are resisted by the Enclave, the Canadians, the rump of independent Washington and yet another nameless hero?
For Cold War nostalgia add in the Museum of Flight and show off some Cold Warriors ala the B-29 in NV as well as other strange air and spacecraft that emerged since the timeline diverged from our own like the DC museum.
The main impetus behind the game being to star fresh with a new land with it's own novel post-apocalyptic flora and fauna without having the silliness of transplanting Southwest fauna and folks like Radscrops, Super Mutants and the Enclave all the way across the continent ala FO3 because the developer is too sacred to alienate old time fans after the prolonged hiatus to the series.
No Radscrops, it's the Pacific Northwest, an evolved Enclave, not just a rehash from the first two games and no Super Mutants since the Master's army is by now a long way away and receding quickly into the past. Add in more unique nuclear freaks, new lore and technology.
Just expand upon the series like NV did, which is sadly all we got from the original FO3/4. That, or set the timeline back before NV and just make the game an FPS Van Buren with as much can be savaged from so much being compressed into NV.