I would just do whatever you like most to do. You can group things together quite easily.

www.si.edu is the Smithsonian website
www.nga.gov is the National Gallery website.

The Marriott Wardman Park is near the zoo so maybe you will want to go there while you are that hotel.

Are your Capitol tickets reserved through a Congressional representative? If not, you can change them easily unless the day is sold out.

Here is a map of the National Mall
http://www.nps.gov/nama/planyourvisit/upload/NACCmap1.pdf

Not an itinerary, but some suggestions for your youngster:
Air Space Museum
Tomb of the Unknown Soldier
Memorials to Lincoln, Jefferson, and both Roosevelts
Museum of Natural History
Memorials to World War Two and Vietnam. I consider it a good thing that children in the U.S. today have no concept of daily war casualty lists in the scores (if not hundreds) of people; and a visit to these sites would be a good way to show this has not always been the case.

The Wardman Marriott sits up on a hill. There is a Metro station right at the foot of the hill. Therefore, you and your son can get anywhere in the city. The zoo is up the street a few blocks. You can go into the zoo before it opens. Great time to see the animals before the crowds arrive.

The Air and Space Museum may be of interest to your son and The Museum of American History would be nice for both of you.

I will be in DC shortly with my 14 year old son. Assuming the weather is nice, we are planning to rent bikes to ride some of the trails and to see the monuments. We plan to use Bike and Roll, which has a location at the Old Post Office Building.

http://www.bikethesites.com/

They also provide guided tours.

I would change those Capitol tour tickets to a more convenient time so that you will have a full day (or most of a full day) on Friday to visit Mount Vernon. You can easily arrange your own tour through the U.S. Capitol Visitor's website, http://www.visitthecapitol.gov/visit/book_a_tour/
Then, I would spend Friday at Arlington National Cemetery, Mount Vernon and, perhaps, Old Town Alexandria.

If your son is studying the Civil War or has an interest in that period of time, then he may enjoy a visit to Ford's Theater. They offer a range of options for seeing the theatre itself and the museum. I have heard good things about the audio tour and there is a special audio tour for kids aged 8 - 12. http://fords.org/home/plan-your-visit/daytime-visits-fords-theatre

Finally, although there are lots of great free museums in D.C., there are some "pay" museums that you and your son might enjoy visiting on Wednesday. My choice would be the Crime and Punishment museum because there are a lot of cool interactive things to do (remotely defuse a bomb, participate in a police line-up, shoot at a police academy shooting range, solve a crime like C.S.I., etc.) The admission fee is a bit steep at $20, but you can get half-price tickets (+ booking fee) through Goldstar. (I used a discount ticket when I went.) Since you will likely spend 3 - 4 hours in this museum, it's money well-spent. http://www.goldstar.com/events/browse/20201
(Look for "CSI Experience at the National Museum of Crime and Punishment)

Goldstar also offers discount tickets to the International Spy Museum, but I don't think it's as fun as the C&P Museum.

What you "should" do will depend on your son's interests. Check out the link vjp provided to determine which of the Smithsonians would interest your son the most. At that age, my daughter liked the American History Museum best, especially the exhibit about popular culture. She also liked the exhibit at the Air and Space Museum that allowed her to "land" a plane on a aircraft carrier. She didn't so much like Arlington National Cemetery, but I think it was important to show her the seemingly endless rows of white headstones and crosses to emphasize the cost of the freedoms she enjoys today. The WWII and Vietnam War Memorials also help emphasize this important part of our history.

Thanks for the replies everyone! Keep them coming. Thanks especially for the tip about changing the capitol tour to Saturday. We would love to spend as much time as possible that Friday out at Mt. Vernon. Anyone taken the cruise there? Is that worth the time?

I did the cruise a number of years ago and the main problem with it is that it doesn't allow you much time at Mt. Vernon. The boat arrives at MV at 10am with return boarding at 1:15pm. That's really not enough time to see the mansion, the grounds, the museum and participate in any other tours (e.g. of the slave quarters) offered that day.

While staying at the Wardman Marriott I highly recommend eating at the Open City Diner http://opencitydc.com/, fantastic breakfast! If your family is active an interesting way to see the monuments would be by kayak or canoe from Jack's Boathouse
http://www.jacksboathouse.com/.

We went when my boys were 11 & 13. Some of their favorite things were the Natural History Museum, American History Museum, Mt Vernon, and the DC by Foot walking tour of the monuments at night.

I cannot recommend the tour enough - you do not need to make reservations - you just show up at the meeting place. The tour is free and then you tip the guide whatever you feel it was worth. The guide was very good, open to lots of questions, and gave plenty of time to take pictures at each place, but also set a good pace.

We had already seen the monuments by day on our own, but seeing them at night with the commentary added so much.

Seeing the monuments during the day and seeing them at night are two different experiences. Although I've seen them many times, I still go back every time I go to DC, both during the day and at night. With the reflecting pool empty and surrounded by an ugly temporary fence, it's not quite as majestic............I'm really looking forward to the time when it's again full of water!

We (Mr. Pickle, our 16yo son, and I)just got back from DC yesterday. We took a Capitol tour through our congressman's office, and my son really enjoyed that, though he liked everything we did. We did a White House tour, the Capitol tour, and visited the Holocaust Museum, the Air and Space Museum, American History Museum, National Gallery of Art, the Spy Museum, and the Library of Congress. I really enjoyed the evening monument tour with DC by Foot. Chris, our guide, was excellent.

If you want to rent a bike, Mr. Pickle got one Sunday afternoon through Capital Bikeshare - www.capitalbikeshare.com - so he could visit the Jefferson Memorial, MLK Memorial, the FDR Memorial, and the Korean War Memorial. He really enjoyed giving his feet a break.

Lee Ann