Guide and information of Japan travel, with access, transportation from Tokyo to Kyoto.
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TOKYO - KYOTO / OSAKA / NARA / KOBE / HIMEJI / KOYASAN
This site would like to explain several routes (No1, No2, No3 and No4) between two most major cities of Japan, Kyoto and Tokyo.
Actually, apart from following 4 options, you may also be interested in JR Tokai Tours . It is package deal including Nozomi round trips plus Sheraton Miyako Hotel, starts JPY22,800 per person for two ways Shinkansen + four nights at the Sheraton without meal, based on three people on same itinerary with three-person-room (JPY23,800 per person based on two people on same itinerary with two-person-room). You would like to make self-organized-tour? Then, here's the way to make your journey wonderful!
No1. SHINKANSEN (bullet train, super express)
In Japanese language, it is directly translated as New-Main-Line (Shin-Kan-Sen). There are 8 lines operated by 4 JR companies throughout Japan, and one of which is called Tokaido Shinkansen connecting Tokyo and Kyoto (and Shin-Osaka) since 1964. Some statistic is available at this official JR page.

Nozomi (Hope) : What goes/runs/travels faster than Hikari (light). We shall better to have Nozomi to live. 2 hours and 30 minutes. JPY13,520. Every 10 minutes or less, which means that there are 6 or more trains every 1 hour.

Hikari (Light) : The fastest object runs in the universe. 3 hours. JPY13,220. There are 2 trains every 1 hour. JR Tokai (JR Central) sells advance tickets called Hayatoku-Kippu as low as JPY11,500 (one week piror purchase necessary).

Kodama (Sound) : Speed of sound is used to be representative of fastness. 4 hours. JPY9,800 (Puratto Kodama).
No2. HIGHWAY BUS by JR
There are more than 10 buses a night and a day each direction. Some of the buses are Josei-Sen-Yo which is female only bus. 8 - 9 hours. Price ranges JPY3,500 (four seaters, two-aisle-two) - JPY10,500 (two seaters, one-aisle-one).

Night bus : Starts JPY3,500 one way (would be as low as JPY3,430 purchased on-line with credit card) which is tight and not that comfortable. Most comfortable seat ever on highway bus can be experienced at JPY10,500 (as low as JPY6,400 purchased on-line with credit card).

Day bus : JPY4,200 or JPY7,300 (as low as JPY5,000 purchased on-line with credit card).
No.3 HIGHWAY BUS by PRIVATE BUS COMPANIES
Other than JR bus mentioned above (No2), there are several private bus operators including Willer Express. 8 - 9 hours. Price varies from JPY3,500 to JPY11,800 one way.
No.4 SEISHUN 18 KIPPU
This page may explain a bit further, but simply saying, this ticket is only available during students holiday time (Winter, Spring and Summer). It can be JPY2,300 one way between Kyoto and Tokyo with best minimum 3 changes as shown below (please note that usually needed 5 - 6 times transfers). Hyperdia would support finding your best time tables.

Tokyo 12:32 - 14:07 Atami 14:14 - 16:53 Hamamatsu 17:02 - 20:08 Maibara 20:18 - 21:12 Kyoto (- 21:43 Osaka, 22:09 Kobe, 22:20 Nara, 22:48 Himeji)
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