The opening scene to Apollo 13 (1995) features a party in Houston with NASA dudes as they gather around the television and Walter Cronkite announces as Neil Armstrong takes his first step on the moon. ( On YouTube )
I was not at that party, but I was at a party in Houston with NASA dudes as we watched the very first moon landing. My dad was a mission control guy with the black horn-rimmed glasses, white shirt and black tie, but Apollo 12, not 11 (Neil Armstrong) or 13 (the one that blew up and barely made it home).
I couldn't walk yet, and I got that the space man on the screen was super important, but at the time I was missing a whole lot of context. The blanks would fill in with time, since the US was super proud of that moment. It's my very first memory.
My first reaction to this question was: hey, I was alive (not by much) when Neil Armstrong walked on the moon. I don’t remember anything about it though.