When we lived in MD, I took many day trips to the Smithsonians with my kids and my scouts.
I think they're all fairly easy to get to from the Metro. Most of them are at the Smithsonian stop (seems right, huh?) but some are more accessible from other stops, so look at a metro map before you just get off at Smithsonian station. I think Federal Triangle and National Archives are two of the close stations. I've put my estimates for a reasonable length of time to see most of the individual museums. This isn't a detailed visit, just hitting the high points of each building, and as always, your mileage may vary!
The newest one is the Native American Museum. It's NOT on the Smithsonian stop, but I can't remember which stop it is off the top of my head. I took both boy scouts and girl scouts there, and it was a really nice museum. I'd say this is about a 4 hour visit, especially if you see the movie.
The National Zoo is also a Smithsonian. It's accessible off the red line, from Woodley Park/Zoo or Cleveland Park metro stops. An insider tip is to go to the Cleveland Park stop in the morning, and walk downhill to the zoo. Then in the evening, keep walking downhill to the Woodley Park/Zoo station. The zoo is about 1/2 way between the two, but at least you're downhill the whole way! They've done a lot of work on the zoo lately. My favorite place there is Amazonia. And the kids like the bug house. I personally hate the gorilla house. I always feel sad when we leave there! But I like seeing the gorillas in their outdoor exhibit. You can easily spend the full day here.
Most of the other museums are clustered around the national mall. Natural History and American History are next door to each other. Natural History has: dinosaur exhibit, bug exhibit, mineral exhibit (including the Hope diamond), a fairly decent section on planets, and other stuff I'm forgetting. This museum (in my opinion), has the most for younger kids. There's more interactive type things there. I chaperoned my sons 2nd grade class there, and they all had fun! I think this is a full day museum too, or at least 4-6 hours.
American History is what most people think of when you mention the Smithsonian. It's got Fonzie's jacket, Archie Bunker's chair, Dorothy's shoes, etc. It's also got the First Ladie's gowns, and a nice section on political campaigns. I remember the kids being able to do a political speech in front of a blue screen, and watching themself. 4 hours would do it for me.
There are several art museums. I'm not big into that type of thing, but here's what I remember. I chaperoned the same son's 5th grade field trip there. Not nearly as much fun for 10 year old boys! There's one gallery that's traditional art, one that's modern art, I think there's a portrait gallery (haven't been there), and an outdoor sculpture gallery. Frankly, the people visiting there were too stuffy for me. I had 4 boys with me, and they were being fairly good, but they were squeaking their shoes a bit. One lady got all huffy and said something pretty nasty to us. For me, 2 hours was enough in any of those buildings, but like I said, I'm not an art lover. We spent about 4 1/2 hours total, and that included a minor lunch break.
Anyway, moving right along. As others have said, Air and Space is a very popular museum. It's all the way at the end of the mall (near the Supreme Court as I recall). There's several airplanes hanging from the ceiling, and a section of rockets. They've got a simulated flight deck from an aircraft carrier, complete with ready room. There's a section of flight test (check out the stuff on Patuxent River, which was where I worked up there). And there's a section on space exploration, complete with a moon rock that you can touch. This is typically a full day museum, but I would break it up since it gets really crowded here! There's also an annex for this museum out near Dulles Airport. I think there's bus transportation out there, but that annex will take a full day to see, just by itself.
In the center of the mall is the Industry building, but I don't think that's open to the public anymore. I remember going there about 15 years ago, but there wasn't much there. Mostly things like the cotton gin and other industrial inventions.
Enjoy!