Perhaps the best opportunity in the National Park System for artistic types are the Artist-in-Residence programs that many parks offer for writers, photographers, painters, poets, and sketchers. And here's a website that can direct you to those programs.
At this site, maintained by the National Parks Arts Foundation, you can see which parks currently are taking applications for this program and learn how to apply.
The National Parks Arts Foundation provides Artist in Residence (A.I.R.) programs to National Parks, workshops and public programs on the arts and exhibitions, and other displays in cooperation with National Park Service.
NPAF is a non-profit 501(c)(3) foundation.
The artist in residence programs are an opportunity for an artist to live and work in a national park, as an artist in residence for a specified term, providing the opportunity to create their art in a national park setting. The artist may be able to present a public lecture or workshop, and may donate a piece of artwork to the National Park Service. Each individual artist in residence program is structured for the park, and specific aspirations of the artist selected.
The artist in residence may be offered a place to live, a studio, use of workshop or lecture space, and interaction with NPS interpretation and other NPS staff.