We're in the DC area. So much to do.
A few hidden things your kids might like but which aren't often advertised: The American History museum has "SparkLab," a room where kids can do hands-on building and science experiments with adult helpers who are there. SparkLab is NOT open all the same hours that the museum is open so go online and check first. Many folks do not even know it's there! Directly across the hall from SparkLab is the exhibit Invention at Play which also has hands-on stuff such as a "sailboard" kids can try to "ride" and things to build with other kids.
Natural History Museum is perfect for you sons' ages. Lots of great dinosaur stuff and if they love dinos there is even a separate little shop with just dinosaur items. Natural History also has a hands-on kids room (also hidden away, also open only specific hours so check in advance) but it does require more interaction from you parents to help them pull out the fossils to handle, show them how to look through the microscopes etc.
Natural History also has IMAX movies, as does Air and Space.
Go to www.si.edu and search their calendar for kids' events at all Smithsonian museums!
Please explore children's theatre in DC! The Smithsonian has a kids' theatre right in the Ripley Building (underground, next to "The Castle" which you'll find!).
Air and Space has a planetarium; be sure to take them to one of the scheduled planetarium shows. If they just love airplanes you need to be aware that the large planes and larger miliitary planes (Concord jet, Enola Gay WWII bomber, space shuttle, stealth plane, etc.) are not at the DC location but are 30 minutes away at the Air & Space Udvar-Hazy Center out in Virginia. Well worth it IF you love planes but you would need to drive out there (admission is free but parking costs). Ask if there is any bus service between the two museums; however, I think the shuttle between them no longer is in service.
If the weather is good they will love walking around the memorials.
Personally I do not think the Spy Museum is for this age at all. We've been three times but my child is older. Most of its kids' programs are for ages 12 to 14 and up. It is very interesting to adults, and if you explain the gadgets etc. your children may find it cool -- for a while. But much of it frankly will be way over their heads -- the history involved is just too advanced for kids this age, and the gadgetry is not demonstrated or something they can experiment with hands-on. There are some hands-on things like tests to see if you can identify the spy among the people on a video, tests to try to decode things on a computer, or if you can "read" a spy satellite image to find the planes on the ground, etc. And there is an "air vent" you can crawl through to pretend to spy on people below you. But that's about it and there is a lot of reading to do for some of these activities.
You could look at the Spy Museum's web site and see if there are any kids' activities on days you are here -- they do have some kids' events and that might be the way to go. But do check the recommended ages. I'm sure four is too young. Because the museum is expensive you might want to be sure it's right for them before you go.
If the cherry blossoms are out when you get here, do go to the Tidal Basin (Jefferson Memorial area) and walk around. Do not try to drive there; there is extremely limited parking. You can walk there from the Mall but be careful -- crossing streets near the memorials area is dicey since local commuters buzz through very fast.
Be aware that food in the museum cafes is very, very expensive. A family of four like yours could easily hit $50 for one casual meal -- by the time you pay from $5.00 to $8.00 for one slice of pizza and several bucks for drinks, you're really adding it up. Choose with care and/or head outside the museums to eat. There is a food court at the Old Post Office building just off the Mall, though I don't know what choices they have there any more. And there is a food court at Union Station (train station) but it is over near the Capitol and not right off the Mall (at least not if you have tired, hungry kids in tow).
FYI regarding another post -- National Geographic no longer has the Saxon Horde exhibit; the current one is about samurai. And yes the Air and Space area where kids get to do stuff with physics is great!
