We were in the DC area a few weeks ago for a show, so we headed to two Smithsonian museums during the day. We always park outside the city and ride the metro in, which is not only easier, but our kids enjoyed. The concert we went to was in Silver Springs, so we parked at that station. Parking was $3 and we were there for about 6 hours. You'll need to purchase a metro card if you don't have one for $2 and then add money to it, or use your apple or google wallet.
We got off at the Smithsonian stop which is on the blue and orange lines. From there it is about a 3 minute walk to both the Natural History Museum and the American History Museum. We were there just after lunch and had no lines at either museum. You will go through metal detectors and have your bags searched. You can't bring in food, but you'll want to keep a water bottle on you. We found no regular water fountains, just bottle refill stations.
Inside the Natural History Museum you'll find dinosaurs, all kinds of animal exhibits, exhibits on light, cell phones, stones and gems, exhibits on Ancient Mali and Egypt, and more. You could spend days at this museum. In the American History Museum, our favorite exhibits were the transportation and entertainment nation. We wanted to see the Wegman's Wonderplace which is for kids, but it is only open 10-4 Wednesday through Saturday.
Most of the museums are open from 10:00-5:30 with a few exceptions. The American Art Museum, Portrait Gallery, and Archives of Art Museum are open from 11:30-7:00 pm. The American Indian and Anacostia Community museums are open 10:00-5:00. The zoo is open from 8:00-6:00 in spring and summer and 8:00-4:00 otherwise. The museums are free, but you will need reserved passes to get into the American American History and Culture Museum, Air and Space DC Museum, and the National Zoo.