The Washington monument from the inside has never been a priority for us. However, we have always enjoyed the view from the top of the Old Post Office building! Is that still an option?
You can get Washington Monument tickets on the NPS.com website for a small service fee. The Old Post Office is closed for renovation; Trump is turning the building into a hotel, but the parks service will retain control of the tower.
Abasket, one of my favorite places to visit is the National Cathedral. Admission is free on Sundays and reduced for students at other times. There’s a wonderful view from the top - just thought I’d suggest it as an alternative to Washington and Old Post Office. http://cathedral.org/
IIRC, the Washinton Monument is closed fir several months because of recurring elevator issues.
The African American Museum just opened, but (free) timed admission tickets have been hard to get. The Holocaust Museum is also free, but requires timed entry. Check this stuff ASAP if you’re interested in going so you don’t get here and are disappointed.
Tickets for a White House tour are arranged through your Congressional office and require submitting SSNs, etc. Do this immediately if you are interested. You can’t take any bags, phones or cameras in the building. No storage available. Kind of a logistical pain unless one person arranges to forgo the tour to hold everyone’s stuff.
The nerdiest tours look like the Segway tours that go by the White House. Everyone seems happy on them. You can also do a Duck tour which will take you out into the river as well as on land. I did one in Boston and it was great fun.
If you’re on the Mall, the food is very good and interesting at the Indian Museum. They only serve “new world” dishes but they are well done. The National Gallery is next best IMO, in that little subterranean cafe that is under a waterfall. It can be hard to find things that are open on the weekend near the Mall except for the Smithsonians themselves and the food trucks that line up on certain streets.
ETA - Cactus Cantina for Tex-Mex and Two Amys for pizza up near the National Cathedral are both really good too. There’s a second Cactus somewhere else in town too. The most Ethiopian food is now in Silver Spring, MD and it is right on the Metro (red line).
Metro rail is very slow and difficult on the weekends and in the evenings most times. I was just in DC and waited 20+ minutes for a train on Friday evening. There is constant track work going on and the best time to take Metro, oddly enough, is during rush hour when they wouldn’t dare interrupt service.
Bummer on the post office but thumbs up for the National Cathedral! I have been there but would love to visit again - and have never been in the tower.
I checked for Holocaust Museum tickets and they do not issue tickets ahead of time after August - you just pick up timed tickets day-of.
Would LOVE to do the White House but since we will be there Sat/Sun/Mon (Columbus Day) I didn’t know if they book weekends. Think I should check? The girls would be ECSTATIC if that happened!
IMO The Holocaust Memorial Museum is a must-see. It is gripping and heart stopping, and absolutely worth your time.
On a lighter note–we lived in DC for 3 years ('97-2001) and really enjoyed going to a few great Vietnamese restaurants. Our favorite place closed, but I’m sure you can get recommendations from the concierge at your hotel or online. Personally, I preferred Vietnamese food more than Ethhiopian.
My D and son-in-law were in DC for grad school (left 3 years ago) and they took us to two places that we liked: Jaleo (Spanish tappas) and Cashion’s Eat Place, which is in the Adams Morgan neighborhood. The menu is eclectic–something for everyone–we went for brunch and it didn’t disappoint.
Contact your congressperson for priority on White House tours. Each representative can get priority spots for a limited number of constituents. But do it fast. Several weeks, at minimum, are necessary.
One of my favorite things to do in DC is to visit the Luce Foundation Archives which are in the building that houses the National Portrait Gallery and the connected Smithsonian Museum of American Art. It is in a very cool part of the building and is essentially stuff that is not on curated display. But for some reason it is great fun to snoop around in the drawers and display cases crammed with uncurated objects. I especially like the drawers full of 18th century portrait miniatures on the top floor in the back on the right-hand side (if facing the back of the gallery space where the glassed-in restoration spaces are). You can also see restorers working on restoration projects.
Since the museums are free you can always pop in and out if the particular museum turns out not to be of interest.
Perhaps the most-visited exhibition at the Smithsonian is the first lady dresses at the National Museum of American History. If your kids didn’t see it as small children it really is great fun despite being something of a cliche. And the American Presidents, and especially America at War exhibitions are directly adjacent and well worth the time. There really is something moving about seeing George Washington’s uniform, or the Civil War uniforms, in person. I realize this is a cliche that many people covered in second grade but there is value in revisiting as an adult. I almost hesitate to mention it because it is so obvious but sometimes cliches are overlooked.
My go-to stop when I have a spare afternoon in DC is the East Wing of the National Gallery (modern and contemporary art) but it is currently closed for renovation.
Here are some images of the Luce Foundation:
^^^The East .Wing is reopening at the end of the month!
https://www.washingtonian.com/2016/04/29/national-gallerys-east-building-date-reopen-september-3-years-renovation/
A couple of things about the White House tour. It can be cancelled depending on what’s going on at the WH that day. You need to call that morning to see if your tour is still happening.
I gave tours of the National Cathedral one summer. It’s a really interesting place. There’s even a bit of moon rock in one of hte stained glass windows, and a gorgeous painting by NC Wyeth in one of the chapels if you are fan of his. (He’s the father of Andrew Wyeth and did the class illustrations of books like Treasure Island, The Yearling and The Last of the Mohicans. It’s out a ways from downtown however (though not too far from Georgetown). If you are interested in changing ringing Sunday is the day to go: https://washingtonringingsociety.org/about/cathedral-practice
I really like the Newseum - since it is not a smithsonian there is an admission charge. Nice view upstairs from their outdoor area.
I also love The Phillips Collection (near dupont circle) - again private so there is an admission charge. They have the wonderful Luncheon of the Boating Party by Renoir.
I love the Newseum and definitely worth a trip. The Smithsonian Museum of American Art and Portrait Gallery are not usually crowded and there is nice cafe in an outside courtyard. I do enjoy the cafe in the National Gallery, very pleasant with the waterfall. Last time I was at the Smithsonian Museum of American History we got to see Julia Child’s kitchen along with so many other great exhibits. Who doesn’t enjoy seeing the ruby slippers??
For a great lunch or dinner break right on the mall (or one block away) try Old Ebbit Grill and you can even make reservations! The food is good and the kids will like it.
Also, the Ford Theater is pretty interesting. Located right near the mall as well. Of course, you must see the American History and Air and Space. Those are my personal favs 
Ford’s Theater now does timed tickets also.
I like the Newseum too, but I’m a media person.
If the Supreme Court is in session, you can tour the building and even sit in on oral arguments for a few minutes. (During the Cohen v. California case in the 1970s about the fellow who wrote “f… the draft” on a jeans jacket, a group of nuns were in the audience)
We were in Washington D.C. as tourists a few months ago. I grew up there but hadn’t been back for many years. We stayed at an AirBnB in Georgetown and took Ubers a few times from there. I would not rent bikes with 3 teens, unless I stayed away from traffic and tourist pedestrian crowds. There are a few places, parks, where this is possible.
One of the best things we did that I had never done before (probably because as a D.C. resident I had no representative) was we stopped at our Congressperson’s office. We didn’t see her, but we did meet most of the staff. You don’t need an appointment to stop in - most of the offices have signs on the door welcoming visitors. After that stop, we almost randomly walked into the nearby Library of Congress. What an amazing place! I had no idea how ornate it was inside that building.