I grew up in Orlando in the early 60s and saw Alan Shepard's launch from outside my first grade school room. Ever since, I've been following the space program. In the late 70s and the 80s, I lived in the LA area, and was actually involved in the space program in a few different ways. I've met a number of astronauts, including the entire Apollo 11 crew (at different times).
The most memorable, and interesting story was meeting Neil Armstrong along with Paul Newman. I was working at the California Museum of Science and Industry (now the California Science Center), and we had several nice spacecraft models. We got a call from someone connected with Ford that they wanted to borrow the models for the taping of a TV show for the 60th anniversary of Ford's founding. Paul Newman was going to interview Neil Armstrong.
We told them that we would have to send some people along to safeguard the models
We got to meet them during a break in the taping. Armstrong was very impressive in his ability to deliver a well-thought out response to the questions Newman asked him without a script.
The highlight though was when Armstrong turned it around and asked Newman what entertainment from that time (the 70s) would be remembered 60 years later. Newman responded "You mean besides Butch Cassidy and The Sting?"
Another highlight from my time at the museum was having dinner with Deke Slayton, and presenting him with a photograph I took of him at a press conference.
I also got to meet with a number of space science and science fiction personalities including:
Carl Sagan
Ray Bradbury
Arthur C Clarke
Robert Heinlein
Jerry Pournelle