I agree with after6's DC suggestions. My favorites of the museums are Natural History, American History (which is worth it just for the exhibit on First Ladies' clothes) and Air and Space. The monuments/memorials are definitely worth it as well, and are in the same area (on the mall). I have actually heard that the tour of the monuments at night is really nice, and with the heat we are experiencing, might be a little more bearable.
I think that the National Zoo is worth a visit, if only to see the pandas--only four zoos in the U.S. have pandas. Like the museums, it is free. It's in a neighborhood called Cleveland Park--he might enjoy lunch at a pizza place called 2 Amys. If he went to the zoo later in the evening and wanted dinner right afterward, a fantastic restaurant called Palena is close by.
Another idea would be to visit the National Cathedral, which is quite pretty. It is in the Tenleytown area, and although it has small restaurants and stuff nearby, it isn't the most exciting area to walk around in.
There are a lot of really great restaurants in DC (those who say otherwise haven't tried eating here in the last 15 years). I would recommend Michel Richard's Central. The food is French with an American twist. It has a more casual vibe than the chef's first restaurant in DC, Citronelle, which is very fancy and very expensive (but if he wants to go for a great, expensive meal, he should definitely try to get a reservation--other great, high-end restaurants he might want to consider would be CityZen and Komi).
Do you know what part of the city he is staying in?
(Oh, and if he wants to see a baseball game and can't get a ticket for the Cubs or White Sox--or doesn't want to pay through the nose--he can catch a Washington Nationals game here in DC. The stadium is still brand-new--only in its second season. Tickets can be purchased for pretty cheap, and he should definitely be able to get something from the box office.)