Kyoto lies a bit between Tokyo and Osaka. It was the imperial city of the crown and has a great deal of history and modernity. Although one of Japan’s major cities, its population is relatively small to the likes of Tokyo.
The Imperial Palace is a great place to start a trip in Kyoto, because you must make a reservation beforehand at arrival. The tours are informative and take you around the entire palace grounds. Reservations require very detailed information including a long application and your passport. Another great sight (quite near the main train station) is a grave yard and To-ji Temple. I really love this temple, because it is very old and very quiet.
My most favorite place in Japan is located a bit south of the city. Fushimi Inari Taisha is a beautiful temple. Although there is a tourist trap at the front, most of the temple grounds are made of peaceful trails through 1000s of tori gates. Some of the gates date back o the 2nd century, maybe even earlier. Entry is free, so why not go?
More Info: Kyoto Guide