National Parks do not allow flyin, launching, or landing on National Park land:
Aviation: Unmanned Aerial Systems | U.S. National Park Service
State Parks as mentioned are under state regulations and they vary from state to state, possibly even park to park.
The good news is National Forests are not locked down:
Unmanned Aircraft Systems | US Forest Service
A quick quote from the above page: The
Federal Aviation Administration (FAA)(link is external) has regulatory authority over all airspace, including recreational use of airspace by model aircraft
(See FAA Advisory Circular 91-57) (link is external). The U.S. Forest Service does not have the authority to establish any additional regulations regarding where UAS can or can’t be flown.