King Street and Braddock Rd Metro Stations are both in Alexandria. Can just buy day tickets and ride the Blue line to Arlington (Arlington Cemetery), then Farragut West (walk to White House). From the White House, you can just walk to the Vietnam Wall, Lincoln Memorial, along the reflecting pool to the WW2 Memorial. From there to the Washington Monument, then you have all of the Smithsonian museums between the Washington Monument and the Capitol.
There are kiosks serving hot dogs, burgers and beer along the Mall east of the Washington Monument. Decent restaurants are to the North of the Mall. Each Smithsonian has some sort of cafe (the Air & Space has a McDonalds). Bathrooms at the Lincoln, Washington Mon, and halfway in between. Each Smithsonian has bathrooms.
So, you can hop on the Metro in Alexandria and be on the Mall and walking around in 30 minutes or less. Great walking. Can even picnic on the Mall if you want. Good family time.
If planning on having a firearm with you, DO NOT GO INTO THE DISTRICT OR MARYLAND. Especially if driving and you have an NRA sticker on your car.
There are some no go areas but it does not sound like you intend to hit any of them. Just be out of the district NLT dark.