My answer would be contingent on a number of variables; different sections of history appeal more to me in some locations, or for some social milieus, or for different defining characteristics, etc., than they do in others.
New York City would have been a blast to experience around 1950-1980. But Bangladesh? Not so much.
If I limit my answer to consider only eras that existed since modern times (which I define as c. 1600 CE—present):
1.) US and West Europe: circa 1960-1980 CE, before everything lost its edge and became commericialised and kitschy.
2.) Europe: around the time of the Enlightenment.
3.) Europe: around the time of the Renaissance.
4.) Americas: during the time of widespread exploration, when everything was an unmolested and novel frontier, just waiting for the intrepid pathfinder or meticulous cartographer with enough serendipity to find it and enough tenacity to trek it.
5.) US and Europe: during the time when one didn't require more than intelligence to be a well-known and well-paid intellectual (such as an author, scientist, mathematician) and when being a successful polymath or adept autodidact was not only possible and economically viable, but laudable.
But modernity kind of sucks—some of its periods suck less than others, but none of them don't suck. I'd much prefer antiquity to any other younger epoch. If I could have both biological immortality and the freedom to travel and explore the world as it existed between the advent of written language (circa 4,000 BCE) and before the terminus of Pax Romana (circa 200 CE), I'd abandon modernity without hesitation for an infinite existence in ancient times.
