As has been stated by others, the architectural highlights include the Jefferson Building of the Library of Congress, the National Portrait Gallery (Old Patent Office), and the National Building Museum. And the National Cathedral. That’s the one you might want to inquire in advance about.
Overall however I generally agree with the proposition that of the world’s great cities, Washington doesn’t have the highest concentration of impressive architectural interiors.
In that respect, I have to say, no. As negative a view as I have of DC, near as I can come to “obnoxious” is that tribute to stone, the Washington Monument obelisk, surrounded by flags. Hopefully that will be kitschy enough for you.
Oh, and do wonder around the perimeter fence of the White house. There is some interesting surrounding architecture there, including the confusing facades of the West wing building and some of the buildings just north.
While you might say there are a lot of displays of patriotism in Washington, I can’t think of any that I’d classify as kitschy.
The Iwo Jima memorial is fairly ostentatious. And the World War II memorial is in my view in bad taste—it looks like something Mussolini would have designed.
But some of the memorials are quite haunting, particularly the Korean War and Vietnam War memorials. I would recommend those two as the first stops for a first time visitor to Washington. And if you’re going there you might as well see the Lincoln, King, Roosevelt, and Jefferson memorials, if you have the time.
The Lincoln and Jefferson memorials always pull at my emotions, but maybe that’s because I’m American. I don’t know whether they would be so meaningful to anyone else.
The height of patriotic display is of course the changing of the guard at the Tomb of the Unknown Soldier at Arlington Cemetery, but that’s rather somber rather than kitschy. The eternal flame at John Kennedy’s grave is worth a stop if you happen to be at the cemetery.
There’s a lot of exterior neoclassical architecture that might be worth looking at, especially in the area around the National Mall.
Mount Vernon might be of interest if you have your own transportation. You can book online, although it’s not usually necessary to do so far in advance.
Except that you forgot the Jefferson Building of the Library of Congress (a true gem on the inside with weekend tours); the National Cathedral (though the Darth Vader gargoyle remains a highlight); the Holocaust Museum; Union Station; the National Shrine of the Immaculate Conception; the Corcoran Museum/School; the National Archives… I could go on.
The number of well-done interiors involving impressive workmanship is more than enough to fill several days of tourism, if that’s what you’re into. You’ve given very poor advice.
For such a quick trip I think you have more suggestions than you can handle already. However, I will add that I have been on tours of both the Capitol and White House, and IMHO the White House tour is a waste of time. You get to see just a few rooms that are unremarkable and with minimal historic significance. A tour of a Biltmore mansion would be superior. However, the Capitol tour was very well done, informative, and you get a sense of what goes on there, especially if it includes a visit to the chambers (Congress was not in session when I went).
Any of the Smithsonian museums would be a good bet depending on what you like, though will be busy with tourist families now that schools are getting out. And they’re all free.
Wander.
About what? 
It’s a nitpick, but I believe the Corcoran Museum was closed. The school is still open, I think. Shame, I liked the museum.
OP has been to multiple in situ holocaust museums. The one in DC is good but I doubt it’s better than what OP has already seen.
Union station, like most of DC’s architecture is far more impressive from the outside.
Also, OP is from Vienna. The one in Europe, not NoVA.
No need to go on. I’m simply not a fan. And every single museum I’ve seen elsewhere is better and more memorable than the ones in DC. Ditto good dining, on average. Maybe I’m just a “hater”.
You might like the Heurich House.
Folks… Vienna, Austria.
I’m all for recommending psychonaut the best DC has to offer. But let’s not kid ourselves. He/She should experience things that he/she can’t find at home around every corner.
I strongly suggest doing the National Mall at night, the Korean War monument is especially moving at night. Plus, the weather will be (slightly) cooler.
You’ve got to be kidding me. If you’re going to tell me that every other museum interior you’ve been to is better than the National Gallery of Art’s West Building, that’s just a joke. Get real.
No, I specifically mentioned the NGA for the interior design and architecture. What I found somewhat lacking is the art collection. I find exhibits in (for example) Chicago, Philadelphia and Boston far more memorable. I’ve not been to NYC for too many years so I won’t mention the Metropolitan Museum of Art and MOMA.
If you doubt me, just check out the upcoming exhibits in the respective cities and compare it to what’s upcoming at the National Art Gallery. Do that periodically through the year to get a better sample.
Only thing I’ll add is if you’re planning on eating at one of our famous fancy downtown restaurants like Old Ebbitts Grill or 1789, make a reservation. Like right now.
The African American museum requires tickets on weekends , but I was there recently and saw people just downloading them on their phones and then going in. There is no need to order them in advance.
The best architectural interiors are the Library of Congress, the Building Museum, the Capitol, Union Station, and the Shrine of the Immaculate Conception.
The Old Post Office used to be interesting but I have not been there since Trump took it over.
Lincoln Memorial and Korean War at night are my favorite recommendations. Especially moving is excellent description of Korean War monument.
Seconded (or maybe thirded?) The LoC is an extraordinary building.
The DEA has a museum at 700 Army-Navy Drive, a block from Pentagon City Metro. Free admission; open every day (10 - 4) except Mondays. The entire building is scheduled to close for renovations starting 21 July.
Oh, and the DEA museum doesn’t need reservations for small groups (15 or fewer) but any visitor over 18 does need a photo ID.