It really comes down to what you define great and where exactly you'd want to live. Living during the golden age of the Roman Empire could be absolutely marvelous, but not if you're one of the countries that is ocuppied by it, right?
In my opinion, the best times are:
Mesopotamia XX-VII century BCE
India XXV-IV century BCE
China I-II century AD
Egypt until II century BCE
Greece VI-IV century BCE
Rome II century BCE - II century AD
Italy XV-XVII
France, England, Russia, Prussia XVIII-XIX
America XIX-1960s