National Museum of Natural History
Kid spaces: Q?rius Jr, a science exploration room best for ages 2 and up. Hours are limited and seasonal, so check in advance of your visit.
Kid-friendly exhibits: all. The Oceans Hall, Hall of Mammals, Insect Zoo, and dinosaurs are classics.
Pro tips: Tickets to the Butterfly Pavilion are free on Tuesdays - go right at opening to reserve yours because they're timed.
National Museum of American History
Kid spaces: Wegman's Wonderplace, a playspace for ages birth through 5 years. Admission is free but timed tickets are given out on weekends. Closed on Tuesdays.
Kid-friendly exhibits: America On The Move - cars, trains, trucks and buses for the transportation-obsessed toddler. FOOD: Transforming the American Table - children will recognize familiar foods from their own kitchens and can learn about where those came from.
Pro tips: Confusingly, the Smithsonian metro stop is not actually close to most of the Smithsonian museums, especially if you need the elevator which is located on Independence Ave. The closest metro to American History is actually Federal Triangle.
Air and Space Museum
Kid spaces: How Things Fly, a children's exhibit on flight. Most displays and activities are aimed at elementary age children, but younger kids will enjoy climbing in the pilots seat of a plane, and pushing buttons, turning knobs and exploring the many interactives.
Kid-friendly exhibits: the open lobbies at the ends of each wing of the building have larger items (planes, rockets, etc) on display and are very kid-friendly. The Pioneers of Flight exhibit on the second floor also is very appealing to children.
Pro tips: L'enfant Plaza, directly behind the museum, is a hot spot for food trucks, so skip the expensive cafeteria and grab lunch al fresco.
National Building Museum*
(note: the Building Museum charges admission)
Kid spaces: The Building Zone - a playspace for ages birth through 5 years, timed tickets; Play Work Build - a construction play area for elementary aged kids. Smaller children can enjoy building with the big blocks, too, but note that some toys in this area are small enough to be choking hazards.
Kid-friendly exhibits: The above exhibits are likely to take up all of your visit, but other exhibits can be accessible to kids as well, especially special/temporary exhibits.
Pro tips: The Building Museum has a large-scale, interactive installation in the courtyard every summer - recent installations have included a huge ball pit, cave like pyramids with explorations of echoes and sound, and an arctic scene with "ice" slides. Tickets are extra $ but usually worth it! They also host weekly storytimes put on by the DC Public Library.
National Gallery of Art
Kid spaces: none
Kid-friendly exhibits: In the West building, check out Degas's Little Dancer, Cassat's mothers and babies, or the only Da Vinci on display in the Americas. The newly renovated East building has modern art and is more kid-friendly, with large sculptures, Alexander Calder mobiles, and pop art exhibits. In nice weather, head west to check out the Sculpture Garden full of art, a cafe, a huge fountain in summer and ice skating in winter!
Pro tips: Make sure you check out the basement level for a great kids' gift shop, cafeteria, waterfall, and a starry, sparkly tunnel walkway between buildings.
National Museum of the American Indian
Kid spaces: imagiNATIONS - a play space best for kids 2 and up. Closed Mondays.
Kid-friendly exhibits: Our Universes - mythology and traditional storytelling from various tribes and nations. Children enjoy hearing recordings of oral histories and the starry ceiling representing Native constellations.
Pro tips: The NAMI's Misitam Cafe is rightly famous for serving up dishes from Native cultures throughout the Americas.
United States Botanic Garden
Kid spaces: The Children's Garden is a newly redone, outdoor children's playspace best for walkers and up. Children can plant, dig and water to their heart's content; explore a large climbing structure; and play in the misters. Only open in summer; be sure to bring a change of clothes!
Kid-friendly exhibits: All.
Pro tips: The botanic garden puts on a holiday display of miniature trains and models of local landmarks every December. These exhibits are extremely popular, so go as early in the season as you can, preferably on a weekday.
US Postal Museum
Kid spaces: none
Kid-friendly exhibits: Most of the exhibits downstairs are kid-friendly and interactive. The highlight for most kids is the full sized truck cab they can climb in and "drive", but there's also a walk-in train car, a mock package sorting center, a stagecoach they can ride, and many interactives throughout.
Pro tips: This is one of the hidden gems of DC - if you're going to be in the city at a particularly busy time (school vacations, 4th of July, etc), this is a great museum to visit for some quiet.