I found the Museum of Natural History to be the best of the Smithsonian Museums. Enter from the Mall into the Rotunda, where one of the largest known elephants is on display. The top sights include Dinosaur Hall; the Hope Diamond (the world’s largest diamond) and other spectacular jewels; the world’s first living coral reef in an aquarium, and, what with global warming killing all the coral in Nature, soon to be the only place to see a coral reef; and the Blue Whale (in the room behind the coral reef display), a life sized model of the largest animal ever. Dinosaur Hall has a monster Brontosaurus, but you will be amazed by the size of the Blue Whale in comparison.
Arrive at the Hope Diamond by the Hall of Minerals, as interesting collection of minerals of the world, and leave by the other entrance to the room where the jewels are to see the world’s largest intact meteorite. The museum also has a number of dioramas depicting scenes of wildlife from around the world. These are pretty good. The collection of stuffed birds is a mind boggling display of the variety of nature– who knew there so many birds? The mounted display of Butterflies is remarkable, especially the ones with psychedelic wings.
There are several galleries of native New World culture– dioramas, totem poles, Aztec calendars, Indian handicrafts, etc. Parents can dump, er, leave their kids at the insect petting zoo while they explore the museum, but the zoo is worth a quick look for everyone.
Opposite the Rotunda entrance is a flight of stair and an escalator going down to the Constitution Ave. Entrance. At the bottom of the stairs is an impressive stuffed Tiger mounted in a leaping position. The lower level entrance lobby features rotating displays that are almost always of interest. The best display the Smithsonian ever had was a large room in the Natural History Museum called "Splendors of Nature". After decades on display, they replaced it, the biggest mistake the Federal government ever made. A small part of "Splendors of Nature" remains on display in this lobby.
The Smithsonian Members’ Dining Room is also on this floor. If you subscribe to the Smithsonian Magazine, you are a member. Bring your membership card(or the address label from a copy of The Smithsonian Magazine) for admission to the Member’s Dining room for lunch(from the Constitution Ave. entrance, bear right past the escalator to the Auditorium lobby, and right again the Dining Room). This is some of the best food available on the Mall, and the only buffet all-you-can-eat lunch. It is especially crowded on Sundays. It’s not immediately apparent, but there are two identical serving lines on the long counter, one starting at each end and meeting in the middle.