Our collection only goes back to 1938. We have 1938-1959 under "National Geographic Magazine" and then 1959-2001 (or so) as "National Geographic". From there on, our collection is entirely digital.
I did a Worldcat search, and it says that the Huntsville Madison County Public Library has it back to the dates you need, but then I did a search on their catalog and got nothing. It might be worth it to call them (256)532-5940. I think they also have digital reference on their website: http://hmcpl.org.
Other hits that do seem to have it that are not terribly far away include Jackson State University: