Is there any quests for each of the buildings in the mall or significant modern day buildings in DC? I did head of state for the lincoln memorial, the main quest for the washington monument, etc but i'm in the Capitol Building and don't see anything of importance. So is there any that relate to recollecting pre-war history and such like what you did at the Temple of the Union or with the museum at Rivet City?

Theres a few quests.

Some are unmarked, some that go along with the main quest line. In the museums theres some of Lincoln's gear and Underworld has multiple quests associated with it.