This is probably one of the best of the Smithsonians (though they're all good). This museum is really large with so many cool and lifesize displays of ancient and extinct animals from different eras. There's insects, modern animals, an aquatic section - all with animal displays. Aside from that, there's a large display of minerals and fossils, with the most notable being the Hope Diamond - the largest blue diamond found.
This museum is located right on the National Mall and is very close to many of the other Smithsonians. It's also close to many of the memorials, so it's a great place to stop and take a look around. Be warned though, because it's got lots of displays and things you can touch, there's lots of kids and families running around.