The National Park Service in August 2014 made it illegal to launch, land, or operate unmanned aircraft under 36 CFR 1.5, which essentially gives the National Park Service the authority to impose public use limits such as hours of operations or not walking off the path.
However, there is a chance you can still fly your drone there. Purposes such as scientific study, search and rescue operations, fire operations, and law enforcement can operate under written permission from National Park Service administration.
No matter what National Park you want to fly in, contact that park’s specific management team well in advance and explain what you need to do. It would help if you can prove your case and professionalism. Ideally you would have a Part 107 certification from the Federal Aviation Administration to prove you are a licensed drone pilot. If you don’t, get it first!