In the Hall of North American Mammals, there are large dioramas of stuffed animals in recreations of their natural habitats.
There is also a hall of African mammals. Here my dad examines an ostrich and a pride of lions:
There are lots and lots of dinosaur fossils.
There is a whole room filled with various gems and minerals.
Perhaps my favorite section of the museum is the "California History" section, which includes a timeline, artifacts, and more dioramas depicting California's human history, from native Americans to Spanish missions to American conquest.
If you are feeling overwhelmed with the problems of your life, I recommend visiting the Natural History Museum, because it really puts things in perspective. The oldest things there are the minerals, which are billions of years old; the next oldest are the dinosaurs, who roamed these lands millions of years ago, then mammals, then humans, who are relative newcomers to this place, geologically speaking. While it is astonishing (and almost impossible) to think that the ground where you are walking has existed for literally billions of years, it is also strangely comforting.