National Recreation Areas allow powerboats on lakes and roads for vehicles, so can drones fly in this area? Can model aircraft fly in this area? Can model boats be used on the lakes or rivers? Can rafts be used in the rivers?
The operation of UAS in these areas is regulated by the National Park Service, but, according to a 2014 memorandum, this authority has been delegated to the individual parks themselves. You would have to check with the park itself. Further information is available in an NPS article on the topic and in the NPS rules and regulations section.
For an example on the state level, the Pennsylvania Dept of Conservation and Natural Resources has designated flying sites in six flying sites at a selected number of state parks. If I go to the website for the Allegheny Portage Railroad (a park managed by the NPS), they have a specific statement on UAS usage in their policy compendium.
Boats and such...that I'm less sure of.