Let's see... Everywhere has its downsides. Still, places I would like to spend a lifetime in:
Athens during its golden age, when it was the hub of western culture.
Rome during its second golden age, around the reign of Hadrian; or in the decadence just before the collapse of the Republic.
There's a sort of lacuna in places I'd like to visit during the Christian Era, everything gets a little bit restrictive, primitive and dull. Possibly renaissance Venice; certainly Mediaeval Russia, which was anomalously socially free during a time of widespread oppression and fear.
One of the trade hubs of the Mongol Empire, along the Silk Road - maybe Samarkand.
Among Native American tribes in the Pre-Columbian era, to experience them before Western influence.
With the very earliest tribal nomads to come to Europe, at the birth of culture and the meeting of Homines Neanderthalensis and Sapiens - those tribespeople who spoke Indo-European.
Further back still, among the tribe who spoke the language from which all modern languages are descended, and therefore whose cultures and customs are the progenitors to all human activity in the world - the people whose modest, daily lives determined the course of history.
Perhaps in Babylon at the height of its power, to see the splendors of the civilisation whose many categorical and empirical lists are the ancestors of all modern scientific literature.
In Persia, during the Achaemenid era, in the royal cities of the east.
And, of course, in the transhuman future; where I fully intend to live in all of the above.
In any of these but the last, my life would be that of something of a social outcast. Really, it depends on one's status. In Athens, whether one was metic (as we would be were we to travel back in time) or a citizen would greatly influence one's experience of living there, in Rome the same applies to the distinction between the free and the enslaved, in Babylon we, as lone foreigners, would be pushed to the outskirts of city life, dwelling in the hazy space between "us" and "them" inhabited by prostitutes and the insane - really, the question is, what time period would you prefer to live in and what would you prefer to be there.