Nara, a city even older than Kyoto.
Nara has the distinction of being the first permanent capital of Japan. Prior to this the capital of Japan was located where ever the emperor was residing. However from 710 to 784 Nara became the permanent capital of Japan and became a large metropolis of shrines, temples and dwellings.
The Nara period was when Buddhism became firmly established alongside the Shinto religion. The city also has the distinction of having the world´s oldest wooden building at Horyuji Temple and also the worlds largest at the great Todaiji Temple.
Nara is a rarity in today´s world, an ancient city with ancient wooden monuments that in spite of Japan´s lengthy and somewhat violent history, has managed to keep most of its treasures and historical buildings intact for all to see and enjoy.
I would say that at least several days are required to see all of the treasures of the city I would also say that Horyuji and Todaiji temples should be at the top of the list. Although because of the age and vulnerability of these temples close inspection might not be possible depending on the number of visitors at the time of your visit.
Don´t expect to get close in March / April in Cherry Blossom season, its madly busy at this time.
Nara also has an amazing photography museum which is located next to Shinyakushiji Temple. It houses the negatives and images as well as a personal collection of work received as a gift to the city of Nara from the late photographer Yasukichi Irie who was a resident of Nara and who captured images of the city, its religion and culture. The museum won the Japan Art Academy prize in 1992.
If you want to take a guided tour of the city then you can take the tour bus with an English speaking tour guide, this takes in Todaiji Temple, Kasuga Shrine and Nara Park. Ask at your hotel as the tour runs from most of the larger hotels or from JR Nara Station or Kintetsu Nara Station.