Remember, Flying Drones is usually prohibited within all National Parks, National Forests, many State Parks, Stadiums, or Racetracks with ongoing events, Military Bases, Prisons, even many city parks.
I live in York County, VA, and the county prohibits Drone flying from all county property, that's School Yards, Parks, Sports Fields, and Public Boat Launches.
The rules usually say that flying in a specific area is prohibited (that includes taking off, landing, and piloting the drone).
However, the FAA controls the air and flying over these areas is not prohibited or even illegal. You just have to fly (as in control…) your drone from outside the specific area. That means flying FPV in many cases… I am no expert on the legality of flying FPV verses within the FAA rule, "Keep your drone within the visual line of sight or use a visual observer who is co-located (physically next to) and in direct communication with you."
But keep this in mind, if you crash your drone, due to any number of reasons, hitting a tree, a bird strike, drone failure (mechanical difficulty), dead battery, etc… You have technically landed your drone and as the old saying goes, "Any landing you can walk away from is a good landing…" But joking aside, if your drone lands (or crashes) within the confines of the prohibited area, you may find it impossible to recover it. Your Drone sitting within the confines of a prohibited area is "prima facie evidence" that you broke the law.
So, if after all this and you decide to try your luck and visit the Washington Monument late at night and get a great nighttime video of the monument and post the video on line and the National Park Service sees it and they might decide to make an example of you. Remember, a lot of folks were convicted for the attack on the Capital due to their predilection to posting videos…
So, when start Droning, Drone Safely.
BDC