According to this Fox News article, he was inspired by the nature of Alaska:
His pal Joan Kowalski, president of Bob Ross Inc., told Fox News that it was during the star’s time in the Air Force that he fell in love with the Alaskan landscape, compelling him to paint.
“First and foremost, he was stationed in Alaska and that landscape just moved him with the incredible mountains and snow caps,” she explained. “Those paintings that Bob [made], those are real, incredible scenes that you would see in Alaska. And that really affected him being stationed there.”
Update per OP's request to add the exact location:
From the book Happy Clouds, Happy Trees: The Bob Ross Phenomenon by Kristin G. Congdon, Doug Blandy, Danny Coeyman:
Ross, who joined the US Air Force in Florida at the age of eighteen, was not only a bartender, but a medical records technician at the Eielson Air Force Base, about twenty miles outside of Fairbanks.
Another location based on this New York Times article:
he took his first painting class at the Anchorage U.S.O. club, became hooked, and spent years going from art class to art class.
Furthermore, one of Bob Ross' famous works is the painting of Mount Denali also known as Mount McKinley which is the highest peak in Alaska:
Mt. McKinley painting on IMDB