The 'Mall' is the long green park between the Capitol and the Lincoln Monument. At either side of the Mall, closer to the Capitol, there are several museums, which the kids can enjoy. All the museums are free! Best for kids: the National Space and Air Museum and the Natural History Museum. They are almost in front of eachother.
Washington DC also has a great zoo, with many different species (tigers,pandas, elephants, jiraffes, snakes, etc) , which is also free! It is not near the 'center' where the 'Mall' is, but there is public transport.
http://nationalzoo.si.edu/
Another pretty area is Georgetown, with its 'main street' which is lively, but that might be more interesting to adults than kids.
Enjoy!