Last time I made a graphic describing the direct flights to Kansai Internation Airport and their times.
This time I decided to make one for traveling to Kyoto from other parts in Japan. For this map I picked several cities including Sapporo (Hokkaido), Tokyo & Yokohama, Osaka, Matsuyama (Shikoku) and Hakata (Kyusyu).
As you can see, except for a trip from Hokkaido, the Shinkansen (bullet train) is usually the best choice. If you are a traveler from a foreign country, you will be able to purchase a JR Rail Pass which you can use for most JR lines including Shinkansens (You need to pay extra for Nozomi).