A meteor heads towards Washington D.C.

The Supreme Court Building is another example of a landmark that isn’t as old as people think. It was a New Deal project and it’s only seventy-eight years old. For most of the its history, the Supreme Court conducted its business in the Capitol building.

The data in the National Archives is redundantly backed up in several places. So, I wouldn’t protect it. Much as I would like to save those wonderful and irreplaceable artifacts in the Air and Space Museum, I would choose to spare a national symbol for solidarity after the disaster rather than preserve the Museum (goodbye, 1903 Wright Flyer).
The White House is the home of the President but it is not the seat of government.
That would be, in my opinion, the US Capitol building. I would protect it.

It’s not really clear what all is actually in the National Archives Building–the originals of the Declaration of Independence, the Constitution, and the Bill of Rights, along with a copy of the Magna Carta and other historical documents. Those are all priceless artifacts of course, but it’s not like everyone’s Permanent Record would be lost; all the actual files pertaining to the business of government are in bland modern buildings in the suburbs.

I voted for the Jefferson Building of the Library of Congress, just 'cause it’s an incredible building and is no doubt also chock full of priceless historical artifacts.

This.

You know a good Doper is going to look for a loophole for the situation as presented. I have a couple for you. An isolated meteorite that only destroys single buildings wouldn’t pack enough punch to obliterate everything under it or even inside of it.

That is a key flaw in the complete obligation alternatives. The main National Archives building is most famous for displaying the Declaration of Independence, the original U.S. Constitution, and the original Bill of Rights. All of those are mounted in display cases attached to elevators that move them into secure underground vaults every night as well as in cases of emergency. They are designed to survive localized bombing even when on display and threats up to nuclear war when secure in their vaults. Security personnel can send them down to the vaults for security at any sign of a threat. The meteorite may destroy the building itself but the really famous documents should still be able to be recovered.

For the Smithsonian Museum of Natural History, one of them most famous exhibits is the Hope Diamond. I will need an expert opinion but I don’t think the meteorite as described will destroy or even mar it at all. It may be difficult to locate and recover the Hope Diamond from a completely destroyed building but I think it would also survive just fine as well.

In all honesty, I’d save Ben’s Chili Bowl. That is some damned good eatin’.

Diamond is carbon.
What about the heat?

All I would care about is getting my fat ass on the other side of the Appalachians before the rock hit.