I should say at the outset that we had super duper good luck with weather, transportation, parking and, really, everything so I can't overlook that but it was an awesome trip.
How about some specific recommendations for families?
The Air and Space Museum AT DULLES. Parking is free after 4 (but arrive by 4:30 for the tower tour that we missed) AND it's open late (till 6:30 I think) in the summer. It was nearly vacant save for the helpful employees and amazing planes. The Space Shuttle was there. It's so different up close. Of course, since it's Smithsonian, it's free entrance for everyone.
The Renwick. This is Mr. H and my favorite museum. We squeezed in only about 45 minutes at the Renwick (it's small so that wasn't too bad). Even the kids liked it. I was amazed how into the art they were.
Random military music and parades. I'm sure the organized traveler would be aware of this but we happened upon a full, free, concert at the Navy Memorial on Tuesday (and found outdoor seating at the burger and brew place next door) and found another concert Wednesday night on the Capitol steps. There seem to be military bands playing and singing every night all over the place. So cool.
Mount Vernon. Unexpectedly awesome. The live demonstrations of boat building, fish net tying and wheat threshing were amazing. And then we drove down the road to the new(ish) gristmill and distillery and that was super cool. We lucked into a private tour--I guess it was a slow day.
Uber. I know. I'm years behind, but we parked it a random lot far away from city center (only $9 for the day) and took our first Uber right to the Mall. It was SO CONVENIENT. Fit all four of us just fine. Cost $6.26. Took 15 minutes. Highly recommend for families (of up to 4). Honestly easier and cheaper than the metro.
Eastern Market. (unrelated to above photo) I don't know if that's the neighborhood name or just the metro stop name but just off the metro there is a street of cute restaurants. They have fast food if you have kids but if you can go sans kids (or have good restaurant kids) there are tons of little cafes and restaurants with sidewalk seating. We were very jealous as we walked by of the folks enjoying a glass of wine and lovely meal. We picked up sandwiches because we were headed to a performance at Marine Barracks One which is right there and was pretty neat (but better for bigger kids).
The museums of American History and Natural History are predictably awesome and we discovered open two hours late most summer days (so open till 7:30 rather than 5:30). The crowds were a bit lighter and the timing worked for our West Coast adjusted bodies. We didn't have enough time here.
Things to skip:
The cafe at the Native American Museum got good reviews and it was tasty but it was EXPENSIVE and a lot of unusual foods so harder for family (read: picky) eaters. The McDonalds inside Air and Space is cheap and predictable but be forewarned, you can't take the food OUT.
American Airlines. Maybe it was my bad booking, not them, but I wasn't impressed.
The carousel at Glen Echo Park. It is a SUPER COOL carousel but there wasn't much else at Glen Echo and it was about an hour out of the way for us so not sure the 8 minute ride was worth it. But we were still glad we went.
And of course the real reason we were there was family. It was so great to see the next generation of cousins get to know each other. The kids in attendance ranged from 5-12; great ages for DC and for a reunion they will remember.