Several DC museums design programs for its youngest visitors. The Frederick Douglass House offers a great view of the city, so can be a good place to start. The other two locations are close to each other, so can be done at the same time:

Frederick Douglass House
Frederick Douglass' longtime home, filled with interesting historic items, is popular with children.
   1411 W Street SE
   202-426-5961
   9:00 am-5:00 pm, daily (Spring-Summer)
   9:00 am-4:00 pm, daily (Fall-Winter)

Tudor Place Historic House and Garden
This home to Martha Washington's granddaughter complements the Frederick Douglass house with information about Washington life in the 1800s. The House sponsors activities for children throughout the year.
   1644 31st St, NW
   202.965.0400
   Tours given throughout the day, closed Mondays

Rock Creek Planetarium
The planetarium show off the night sky of the District in a afternoon programs for kids. They offer regular shows on weekends and Wednesday afternoons after school.
   5200 Glover Road, NW
   202.895.6070
   Wednesday, Saturday, Sunday shows

For more ideas, visit one of these DC area family resources:
   Our-kids
   Go City Kids
   Washington Parent