The Imperial Palace in Kyoto served as the emperors' residence during the Edo Period in the seventeenth and eighteenth centuries until the Meiji Restoration in 1868. It is not possible to enter the buildings, but the palace grounds can be visited on a guided tour (English tours are available). Tours take around an hour and are free, but it is necessary to make a reservation with the Imperial Household Agency in advance.
When I visited in July 2015, a typhoon was on its way, making for some dramatic skies that contrasted beautifully with the vermillion color of the gates.
Find out more about Kyoto Imperial Palace.