Although I can't speak to what's a good campground to stay at, I have been taking groups of kids (11-14 years old) to Washington DC for 20 years. Yes, I'm one of those teachers who brings the class trip to our nations capital every April vacation. Don't worry though, our trip is from the 16th to the 20th so you wont have to contend with us.
Seeing as you're taking your daughter, I thought I let you know what we take our students to because over the years, we've gone to just about everything in DC. Here's a list of the sites the kids tell us they enjoyed (or endured but were thankful that we took them to it anyway):
- U.S. Capitol Building (exterior)
- Air and Space Museum
- Museum of Natural History
- American History Museum
- Arlington National Cemetery (Tomb of the unknowns, changing of the guards, Kennedy burial sites)
- Steven F. Udvar Hazy Center – the Air and Space Museum “Hanger”
- 3-hour Dinner cruise and dance on the Potomac River
- “Daniel’s Story” – Holocaust Museum
- Washington Monument
- World War Two Monument
- White House (exterior)
- Baseball game (National or Orioles, whichever team is in town )
- Ford’s Theater
- National Archives
- National Zoo
- Jefferson Memorial
- FDR Memorial
- MLK Memorial
- Lincoln Memorial
- Korean War Memorial
- Vietnam War Memorial
- Iwo Jima Memorial
- Six Flag’s America
Since you will be a small party, (Our group averages about 120 people per year.) you might want to consider taking a Segway tour of DC. They look like fun and they take you to most of the places I listed above. If you want to tour things like the capitol or the Washington Monument, make sure you check out their websites. You need to make arraignments ahead of time to get tickets but you can also check to see if they will be giving tours. I believe the Washington Monument is still closed due to the earthquake back in 2011.
I also agree that Baltimore's Inner Harbor is a great place to visit and Fort McHenry is not too far from there, too.
Whatever you decide, I'm sure you'll have a fun family adventure.