“First watch worn on the moon”, that is what the Omega Speedmaster is called until today. It made the watch one of the biggest icons of watchmaking. For more than one reason. Buzz Aldrin wore the Speedmaster as first human on the moon.
Buzz Aldrin’s Speedmaster was lost when it was shipped to the Smithsonian Institute in Washington DC. Where it is nowadays, nobody knows.
The Speedies worn by Neil Armstrong and Mike Collins can be viewed at the Smithsonian Institute, to be precise in the National Air and Space Museum, Washington DC, which is part of the Smithsonian Institute.
While many people think that one of the first three Omega Speedmasters worn on the moon appeared at an auction, I can assure you, none of them ever have.
Proof for that can be found on the Homepage of NASA:
From a theoretical point of view, the watch worn by Buzz Aldrin could be somewhere in private possession. But it would have been acquired illegally.
In the year 2003 a newswriter claimed in this contribution, that someone claimed to own the original watch of Buzz Aldrin. This story proved to be more complex than anticipated.