For some reason all the atomic weapons in the Fallout universe were remarkably low yield. Way less advanced then all the other tech.
One hit the White House and wiped it out completely, but the damage didn't extend much beyond the White House grounds themselves.
I believe I read somewhere that most of the radiation and "fallout" from the war wasn't actually from the bombs that were dropped, it was from the massive number of atomic cars and other vehicles/devices that were in use.
Wrong, the D.C. area was the only location in the world which was fully nuclear powered and upgraded to the newest technologies. The main cause of the recourses wars and eventualy the Nuclear Holocaust, was the nearing total depletion of petroleum, with china having no fancy nuclear technology at all, triggering their invasion of Alaska. The U.S. as well, even with their recently developed fission batteries and nuclear powered cars, didn't have the industry or recourses to distribute these technologies throughout the country, leading them to the brink of complete economic demise, which forced the U.S. into the same conflict as all the other powers in the world. As for the Nuclear bombs, it seems unlikely to me the Chinese wouldn't put an high effort into ensuring to decapitate the U.S. chain of command, focussing a substantial Nuclear arsenal on leveling the D.C. area. Fallout wikia describes the average yield of a Nuclear Warhead in the Fallout universe to be considerably lower than in our own, yet much higher in numbers, even so, their yields amounted to about 200-750 Kilotons, meaning that even one direct hit would have completely destroyed most of Washington D.C. There are only two logical explanations to this, likely the U.S. government had deployed large amounts of anti-aircraft and anti-missile installations, hindering the Chinese - which would have to fly over pretty much all of the U.S. first, or use ICBM's over the Northpole - into reaching the U.S. The other explanation would simply be that the game designers felt it would be a waste to reduce Washignton to smoldering ruins, rather than to leave most of it intact, apart from it's natural decay.