Tokyo (Shinjuku) to Teshima Art Museum

Hi Everyone, I will be in Tokyo on 31st Aug and have plans to travel up to Teshima Art Museum.

Since I'll be staying in Shinjuku, would love advice on how we can head up to Teshima Art Museu from Tokyo.

Do I have to take a rail ride for 8 hours? What will be the fastest way to get there without it being too expensive at the same time? Understand that it's about 30583 Yen just to get there.

Would love some advice, thanks very much!

Take the shinkansen from Tokyo to Okayama and then follow the instructions on the following page:
http://www.japan-guide.com/e/e5440.html#jump_access

Instead of the shinkansen, you have the following other options for travel between Tokyo and Okayama:
http://www.japan-guide.com/e/e5703.html

Alternatively, you could fly to Takamatsu and access the island from there:
http://www.japan-guide.com/e/e5908.html

In any case, it is going to be a long journey.