In late January 1959, Buddy Holly embarked on what would have been a three-week tour, called the Winter Dance Party. Waylon Jennings was playing bass in his touring band, and just before departing the two musicians took these photos at a photobooth in Grand Central Terminal—at least, that's where all internet documentation places the photobooth.
Tragically, Holly (and music) would die shortly after, on February 3rd, when a charter plane he was on crashed in Iowa. Jennings had been bumped from the flight by J. P. "The Big Bopper" Richardson, who had the flu. These are some of, if not the last photos of Buddy Holly and Jennings together.
To confirm these were actually taken at Grand Central, we reached out the MTA about photobooths inside the Terminal, but we were told their historian Dan Brucker was not able to confirm "whether they were there at all." However, our friends at the New York Transit Museum directed us to a few online sources.
An online history of the photobooth notes how in the 1940s "the [photobooth] pictures became even a bigger business with concessions in the NYC subway, the Port Authority, Penn Station, Grand Central and the Staten Island Ferry and at the 1939 New York World’s Fair." Another article is about the Photomatic machines that used to be housed inside of GCT. Those seemed to output images with a silver frame, and most photos we found online from that machine are from the 1930s and 1940s.
These photos seem to be in a strip format, so the machine Holly and Jennings were in was likely an updated photobooth, however, it's unclear when it was installed, where it was located, and when it was removed from GCT.
To this day, if you Google "photobooth" + "Grand Central," you'll mostly get results regarding these Holly/Jennings photos.