IMO, the only redeeming thing about that museum.
Better yet, come back in a few years. The Monument is still closed due to earthquake damage.
Wow, I’m surprised it’s still closed! We need a smilie with a dunce cap. I moved away in 2010 and unfortunately missed the quake. Well, the good news is that you can still get a good view from the Old Post Office (unless that’s also closed), and it leaves you with a bunch more time to do other things.
I’d suggest that you make sure to do the Lincoln Memorial and the Korean Memorial at night. Both are much more dramatic then. I actually wasn’t a fan of the Korean Memorial at all until the third time I saw it, which was at night, and then I marveled at the effect.
Doesn’t Arlington have a very convenient Metro stop? It’s been a few years, but I’m pretty sure that’s how I got there.
Convenient in the sense that there is a metro stop there, but inconvenient in that there’s no direct line there. From the mall, you either have to take the blue line that goes north, west, then south or blue line east to L’enfant and transfer to yellow.
Either way, it’s about a $4 metro fare and upwards of 30-40 mins.
Yeah, Arlington can be a little frustrating to get to–be wary of what sort of construction WMATA may have going on. It’s been a while since I’ve been in town, so they might be done with silver line construction stuff, but their fixes definitely slowed things down in some places last summer.
I wish the Monument wasn’t still closed. The Holocaust Museum is very sobering, but very beautiful. I don’t know that it’s the best thing for a fun family vacation though.
The National Zoo was awesome, if you like animals. It’s a bit of a hike from the metro stop, but a great place. The lions were even awake when I was there in the middle of the day 
If you do plan to visit the National Cathedral, make sure to check out Darth Vader.
I think they’ve just finished assessing and are going to move on the repairs soon. Crazy.
I’m not sure I’ve even done the old post office - I’m going to check that out one of these days.
We very much enjoyed Mount Vernon. About a half-hour away.
We also liked the tour tram. You can hop on and off all day along the circuit. I think there are a couple of them, but we used the one that starts on the corner of the block that contains Ford’s Theatre.
Speaking of the Navy Yard, the Navy Museum is very interesting as well.
Founding Farmers is six or seven blocks from the Lincoln Memorial which I think is too far to go. For food at the Western part of the Mall, there are a collection of food trucks which park on Virginia avenue near 20th. They are there from 11:30 to 2 most weekdays.
There will also be food trucks at Farragut Square during lunch if you visit the White House.
I have heard good things about the restaurant at the Newseum though it may be pricey. The food court at the Old post office building is better than the museum food (except for the Indian museum). Also there is a food court in the Reagan building which is very close to the mall.
Gravely point is great if your kids like airplanes, but it is not metro accessible.
The interior of the Library of congress is really beautiful.
The best cherry blossoms are between the tidal basin and the MLK memorial.
Maybe not a great spot to take kids, but the bar at the Willard Hotel is fun with portraits of many of the famous faces that have imbibed there over the years. Lincoln stayed there when he first came to DC.
The National Gallery East is about to be closed for 3 years for rennovations, so get there while you can. Much of its collection came from a gift from Herb and Dorothy Vogel, he was a retired postal worker. The two of them were not rich, but had a great eye for art. They gave their collection to the National Gallery because it is free to the public. He recently died, they were just lovely people by all accounts.
Here’s a piece of local advice. If you’re asking someone for information, don’t refer to Arlington Cemetery as “Arlington.” Arlington is the name of an entire county.
This. As a native Arlingtonian, there’s much more to my hometown than just a big cemetery. Not that the big cemetery isn’t worth visiting; Arlington House, Robert E. Lee’s home, is on the cemetery grounds and the various notable graves (JFK and the Unknown Soldiers come to mind) are worth a look if you get there on a nice day.
I’m not sure whether it would be of interest for your family, but I’m a big fan of the US Botanic Garden. It’s on the mall (Capitol end, south side) two blocks (east) from the Air and Space Museum, next to the Museum of the American Indian. There’s a large interior space full of jungle plants and the sound of running water and a number of smaller galleries dedicated to different themes (like orchids or dessert flora). When I’m coming down off of a high-stress period, it’s one of my favorite places to just find a bench and relax. Oh and admission is free. As I said, it may not be your cup of tea, especially with kids, but it deserves a mention just in case.
The zoo is definitely worth a look. Do plan on doing a fair amount of walking if you decide to visit; the zoo is about half a mile from the nearest Metro station (which means another half-mile to walk once you decide you’re done for the day) and there’s a lot to see while you’re there. Again, admission is free.
As for stuff on the mall, I’ve been to all of the museums (most of them several times) and most everything is about as interesting as it sounds. (If something sounds interesting to you, check it out; if it doesn’t you can probably skip it.) Natural History is always fun; there’s a little of everything there from dinosaurs to the Hope Diamond. Air and Space was always a favorite until I got my Aerospace Engineering degree and a large section of the museum became the “Review of Sophomore Year Wing”. I was underwhelmed when I went to the Museum of the American Indian but that was years ago and I wasn’t really in a museum-visiting mood at the time. Again, if it looks interesting to you, give it a shot.
I also recommend the tour tram - or at least I would if I was convinced that it was still in operation (the last time I rode the one I am thinking of was in 2003); it looks like the one I am thinking of has been replaced by a double-decker bus, run by the same company (it costs $50/person for two days, and is hop-on, hop-off, but keep in mind that it stops at 6 PM each day).
As for food court-style food, what about Union Station?
Like what? Spider Kelly’s?
Well, we do have the Pentagon and National Airport. And, yeah…
There’s more to Arlington geographically speaking at any rate. The point is, asking a local how to get to Arlington is more likely to get them to ask “Where in Arlington?” than it is to get you directions to the cemetery.
EDIT:
One more thought just came to me. I’ve seen DC Ducks around town before and it looked like an interesting way to see the sights. It’s basically a 90 minute tour of the mall and its surroundings in a WWII amphibious vehicle. I’ve never had a chance to try it but it looks like fun.
Dulles airport is in Virginia. Sorry. 
However, once the Metro comes through, I’d say it still counts no matter what the technical boundaries may be.