What a lucky kid! That will be such an epic trip.
If you can swing it, the best time to visit Washington, D.C. is September through November. During the fall, the weather is much more comfortable and there will also be fewer tourists to deal with. There will be shorter lines at the museums and memorials, too.
The weather is also decent from March to May, but between Spring Break, school tours, business conferences, and seasonal festivals, you can expect a few more tourists than during the fall season. And summer brings in the most sightseers.