"Houston, Tranquility Base here. The Eagle has landed." - Neil Armstrong, July 20, 1969, 8:17PM GMT (3:17PM EST)
This video shows highlights of the live television coverage of the Apollo 11 mission.
Checking with a U. S. Naval Observatory site on Sun and Moon data (hat tip to Chicago Boyz contributor Jay Manifold), it appears that the moon was visible in all the lower 48 states at the time of the landing. Somebody with enough foresight could have pulled off the ultimate photo-op - a photo of someone's living room with the moon visible through a window, with the TV turned on at the time of the landing.
[UPDATE: If the moon was just rising over California, that means it was setting, or close to it, over the Baikonur Cosmodrome. How's that for timing?]
The space race, however, provided a clear-cut competition. And the Moon was the Big Enchilada, since poorly educated people are not much impressed by low Earth orbital stuff, but even African tribesmen are well aware of the Moon, can easily grasp the concept of walking on it and intuitively understand that it's not an easy feat.
The simple fact that the Americans walked on the Moon and the Soviets did not made both the elites and the populations question Soviet claims of their superiority and boastful promises of the inevitable victory in the Cold War.
One cultural legacy of the 1960s space program was the Major Matt Mason astronaut toys. I owned two action figures and Mattel's concept of a lunar rover - the red tractor-like Space Hauler and accompanying Space Bubble, visible at the top left on this page.
July 20, 1969. The Apollo 11 mission was the first live news coverage of an event I remember watching on TV. I was eight years old and living in Gulf Breeze, a town on the southern edge of Escambia Bay across from Pensacola, Florida. My mom still has a 1969 issue of (either Life or Time, I think) featuring this image on the cover. (Other images available here.) Jay Manifold has some musings here.
I recall someone recently commenting that for the 20 minutes that Michael Collins piloted the command module behind the moon as the LEM was on the surface, he was the most alone that any human had ever been. May there come a day within my lifetime when space travel is far less solitary.