Seems to me the biggest issue is why the BoS would ever want to go Washington or even the East coast period. The first and most heavily destroyed cities would be New York and Washington D.C. I promise you in the even of a nuclear war Washington, regardless of whether the president was there at the time and New York would be completely leveled and so irradiated that even after 2000 years it's unlikely that there wouldn't be dangerously radioactive places. Tl;Dr there's no tchnology left for the brootherhood there. I find it far more likely they would try to cross the Pacific (which I imagine would require a boat, given veritbirds likely limited range) in hopes of finding a country that survived mostly unaffected and thus would have a plethora of tech not avalible to them or go up north. After all the U.S. certainly has a few installations in Alaska that are working on some high tech things.