Soon I’ll be travelling to a conference in Austin, and on the way I will be stopping over for the weekend (June 22–23) in Washington, DC. Are there any popular tourist sites there that it is necessary or advisable to make advance bookings for? I’ve already got reservations for a tour of the Capitol. (Unfortunately, a White House tour doesn’t look to be an option; foreign citizens need to arrange these through their embassy in Washington, and mine has not responded to my query.)
The African American Museum usually requests timed entry passes Plan Your Visit | National Museum of African American History and Culture
I strongly recommend the excellent Trip Hacks DC YouTube channel, over 100 short videos covering every aspect of DC travel.
Ask away if you have any other questions, I’ve been there 3 times the last year and am moving there later this year.
The Spy Museum is pretty neat. My husband and I will also be in DC on those days. He’s a librarian and the annual conference is June 21-25.
It would help if you could tell us what you would most like to see. The Smithsonian museums typically don’t require advance arrangements, for example, but if there are special exhibits or times which are particularly popular in a certain venue there may be timed entry, as dalej42 mentioned.
Holocaust museum
The African American Museum has been mentioned, I haven’t yet been, but I hear it is excellent and that the cafe is very good.
Second the spy and holocaust museums.
And you do know that being outdoors in the daytime in Austin in June is like breathing fire, right? Glad you’re coming, have fun, but omigod it’s gonna be a scorcher.
I’ve been to at least a dozen Holocaust-related memorials and museums here in Europe, most of which are located in former concentration camps, prisons, and other Nazi-era sites where the original artefacts and documents can be examined first-hand in their original contexts. Is visiting a museum seven thousand kilometres away from where the Holocaust happened going to add to my knowledge or experience in any way? (Serious question—I wouldn’t have visited all these local places if I weren’t interested in the subject, so if there is a lot new to see or learn in Washington, then I would gladly consider visiting. But if this is just going to rehash the same sort of information, minus the original setting, then I think there may be better places for me to spend my time.)
Vienna’s in the midst of a record-breaking heatwave that has seen temperatures as high as 38°C. Judging from the weather forecast for Austin, it’s going to seem like home sweet home. 
I like touring large, beautifully architected and decorated historical buildings. This was my primary interest in tours of the Capitol and White House. If there are any other similar buildings that I can tour (on the inside!), let me know! Unfortunately the Supreme Court is not an option as it’s closed on weekends.
The Library of Congress has a beautiful interior. There are tours, but no reservation is needed.
Not really, it’s a powerful museum, but similar to others you e been to.
Context Travel (contexttravel.com) offers excellent walking tours that are guided by academics or other professionals. We did one of DC that was lead by a retired journalist that was really informative (and we’re from DC). It might be very humid and hot, though.
I’m afraid you’re in for a dull time. Most impressive looking buildings in DC are impressive on the outside only and access is restricted because most are actually working gov’t offices which you can’t just wonder into without an appropriate security pass. The ones worth seeing have already been mentioned. I suggest you kill 3.5 minutes wondering around the Ronald Reagan building on 13th just north of Constitution (across the street from Dept of Commerce). The National Art Gallery is nice on the inside, mostly the central hall. There’s a brand new dinosaur exhibit that just opened in the Natural History Museum. Supposed to be good. If you don’t mind sweating in the hot sun, see the memorials towards the west end of The Mall. The Korean War Memorial is my favorite. Afraid DC lives up to it’s reputation. All show on the outside, little substance on the inside.
Do you actually live in DC?
OP: you may like the National Building Museum and the Portrait Gallery in the old Patent Office.
Does anyone, really?..
ETA: I “live” in NoVA. I work in DC.
So if we need a tour of an Olive Garden or cul de sacs named after Confederate traitors you’re our guy.
OP didn’t ask for opinions of what to see in NoVA or where to get good Italian food in the D.C. Metro area.
Believe me, no-one is more [del]confused[/del] depressed than I in finding myself still living here.
Well, given that I’m in town for just two days, seeing just two or three buildings from the inside, and a few more from the outside, is probably going to be enough.
I’m also interested in kitchsy or obnoxious displays of patriotism. Is there anywhere particularly good for that?
The main attractions have been covered. One place I recommend to visitors is Dunbarton Oaks
https://www.doaks.org
It is a former elegant home in DC that has been turned into a private museum. It was the site of the initial meetings that led to the establishment of the United Nations in 1944-45.
It is definitely off the beaten path and has never been busy when I visited.
The African American museums takes walk up visitors on weekdays now according to a news report I read. Timed entry were still available to bypass the lines and were still required on weekends.