The Smithsonian is actually broken up into a number of buildings: Centennial Hall, which houses a collection of industrial equipment, household goods, and other items from the 1876 Centennial celebration. There is also the Natural History Museum, which has about 3,000 dusty stuffed animals (I mean taxidermy, not Beanie Babies), giant insects on pins, an anthropological history of mankind, and the really interesting part: gems and minerals display. There are other parts as well.
The National Gallery of Art (East Wing by I M Pei houses the modern collection, classical West Wing houses the older stuff) has a lot of good stuff on display.
Air & Space is actually interesting to non-propellorheads, even, so if you've never seen it, give it a try. It's not hideously crowded during the weekdays. See the iMaxx movie To Fly if you can.
The Giant Peach is just a water tower by I-90 (or whatever the main highway os down there), shaped like a peach (complete with stem and leaf) and painted appropriately, sitting on God's Own golf tee. If I can find a picture from our run home with the ACR, I'll scan it.