Here are a few tips that help you find some hidden gems:
1. Consider getting Capital Bikeshare keys during your visit and bring or buy bike helmets. Unlimited 30 minutes trips for about $7/day. Download the app "Spotcycle" so you know which stations have bikes and docks. Cycling around lets you see so much more and so much faster. You can bike from the capitol down to the monuments in 10 minutes and then drop the bikes off at a station while you explore. You can bike around the Tidal Basin over to the Jefferson Memorial and be back to Lincoln in great time. Not necessarily what you want, but you can fit a lot more in if you're only walking once you get somewhere instead of walking to and from every sight.
2. Call your congressperson now and ask for a tour of the white house.
3. Ditto for the Capitol, but you can also go on tours without congress invitation.
4. If you're near the Capitol, also see the Botanical Gardens across the street. Cross Independence, and have lunch at the Rayburn Office Building Cafeteria. You have to show ID to get in, but once inside, the cafeteria is really nice and unbelievably cheap.
5. Newseum -- this may be the best museum in the city for kids and adults. But it's not part of the Smithsonian, so it's not free.
6. Library of Congress. Most beautiful building in DC in my opinion. The tours focus on architecture and history.
7. See what's going on at the Supreme court. See if there are any protests and join in! Everyone should take part in a protest at least once in their life (either as a participant or spectator) to experience how important our right to free speech is.
8. Check out the Events Calendar on the Smithsonian website (closer to your visit, as more events come online each month). Have each member of the family choose events that are of interest to them. If lucky, there will be some free special events during your visit. I check out the calendars quarterly and find all types of interesting free lectures, films, panel discussions, exhibits, etc. that few tourists now about.
9. Don't assume you know that it will be cold until you get here. This year, honeysuckles bloomed in February! (I know because my rose bushes get trimmed when the honeysuckles bloom).
10. Secret place: State Department website offers tours of the reception rooms. It's common to get bumped for someone important, but it's worth a try. If it looks like something your family would really enjoy, sign up for a tour every day and then if you actually get one, drop the others.
11. If you want a few hours of bike riding, take a ride on the Mt. Vernon trail. For this, I'd do a bike rental from your hotel because bikeshare gets expensive for all-day affairs.
12. Need a break from the walking? See an imax film at Air and Space or Natural History.
13. Look up the "Circulator" as a public transportation option. $1 rides and transfers. Really easy.
14. Personally, I would not stay in Georgetown. It's not "the" place to be anymore. It's hard to get around, the traffic is horrific, it's expensive, and it's almost a 'has-been" location. I live near Capitol Hill-Navy Yard (Near Southeast, Capitol Riverfront) neighborhood. Lots of new hotels here in 15 minute walking distance to the Mall. Super easy to get around in this area by foot, by bike, by Metro, by Circulator, and even by car. You can hop in a car and get to the airport in 6 minutes.
15. Check out the video for this neighborhood to see if this would be your kind of place. This video is a few years old, and it's even better now because it's more built out.
http://www.capitolriverfront.org/#16. Also, check out Frederick Douglas museum, Barrack's Row, O Street Mansion, Embassy Row,
16. Keep posting because I'm sure you'll find more between now and Feb.