I worked at NASM from 1984 to 1996.
Unfortunately, you have picked literally the two busiest days of the year to visit. I assume that being there on the day before Thanksgiving, or even better, Thanksgiving day itself, isn’t possible? Thanksgiving is practically empty (although they may close early–check on that) and the day before, while more crowded than Thursday, is much less crowded than Friday.
If crowds bother you, you might want to consider doing Udvar-Hazy instead of the downtown museum. I left long before U-H opened, but I’d guess that although Fri-Sat will be its busiest days, too, it’ll be much less crowded than downtown. You can pretty much see all of U-H in a couple of hours, because as JerH said, it is only planes with very basic labels, no exhibitry to speak of.
A warning about U-H: admission is free, but parking is $12 per car. There are no free parking options. There’s a shuttle from the downtown museum that costs something like $7-8.
If you’re set on downtown, as others have said, the must-see artifacts are in the main entrance hall, called Milestones Hall. The Apollo 11 command module, John Glenn’s Mercury capsule, Yeager’s Bell X-1, the X-15, and just unveiled, SpaceShipOne. And the only moon rock in the world that you can actually touch. It’s easy to miss, in a tall pillar near the center entrance on the Mall side.
The 1903 Wright Flyer has been moved to an exhibit on the Wright Brothers on the second floor.
First thing when you get in, go to the box office for the IMAX theater and get a ticket for a film. Shows will sell out early. If you’ve never seen To Fly! it’s definitely a must-see. You can probably see most of the other films on NASM’s schedule at your local IMAX theater, but not To Fly!
Buy a ticket for a later show, so you can take a load off your feet after wandering the museum for a few hours. You might also want to consider a planetarium show (second floor across Milestones from the IMAX theater on the first floor). Although it’s overshadowed by the IMAX, it’s one of the biggest and best planetariums in the world.
Take a good look at the big Robert McCall murals on the walls to either side of the south entrance hall, where the information desk is. Look up: there’s the Voyager airplane that Dick Rutan and Jeana Yeager flew around the world non-stop, unrefueled.
Don’t miss the Sea-Air Operations Gallery, Gallery 203, second floor, northeast corner. It recreates the hangar deck of an aircraft carrier. And as you walk in, take a long look at the huge model of the aircraft carrier Enterprise, built by one man over the course of 12 years! It’s in a large case on the walkway between 203 and 205.
I also like Apollo to the Moon (209). But it’s been so long since I worked there, and they’ve changed a lot of the exhibits, so I won’t go on more about them. There’s plenty to see, and you can easily spend a whole day or more there if you’re a serious air/space buff.
Do not, repeat, DO NOT, eat in the McDonald’s in the museum. It’s just a McDonald’s, but the prices are about twice the norm. Walk out the south entrance two blocks and turn left on C Street. There’s a decent restaurant in the Holiday Inn, and there used to be a deli and a (normally priced) Roy Rogers on C between 6th and 7th. I can’t assure you they’re still there, but I’d wager you’ll find something.
If you and your wife want to split up, the National Gallery of Art is directly across the Mall from NASM, and the National Museum of Natural History (Hope Diamond, big elephant) is also on the opposite side, down toward the Washington Monument. Past NMNH is the National Museum of American History (First Ladies’ dresses, Ruby Slippers, Star Spangled Banner). Of course, all those museums will be packed like sardines, too.
If you want to go to a less-crowded museum on the mall, try the Freer Gallery of Art and Sackler Gallery “Asian art and a specialized collection of American art.” It will be having its busiest day, but will be empty compared to the Big Three.
If you’re driving up, parking near the museums will be a problem. You may want to consider parking at New Carrollton or another outlying Metro station and taking the Metro in. If you’re taking Metro, get off at the L’Enfant Plaza stop for NASM, not the Smithsonian stop. It’s all the way down near the Monument and NMAH, and a very long walk to NASM.
You can use the SI Web sites to sketch out your priorities and plan your visit in advance.
Have fun.