This is a tough one for me because I'm such a history nerd. I think for me it's a tie between Greece anytime during the height of their empire and France in the mid 1800's.
For about 500 years BC, the Greeks were doing things that no one had ever imagined. They invented so many concepts and practices and devices that we still use some form of (or all of) to this day. Scholars were making prolific and important statements, inventors were creating life-changing devices, and artists were making some of the most revolutionary works the world had (and has) ever seen. What a time- oh! to have been able to play witness to such an incredible movement.
In 1800's France, the Bohemians were just surfacing (go see La Boheme by Giacomo Puccini if you want to learn more) and starting to make big, big changes. There was this very "devil may care" attitude among many young Parisians, and Bohemian writers and artists and musicians were also doing important things. But mostly, I just think it was a blast to be alive.