Japan’s superexpress train, the Shinkansen bullet train came to Hokkaido on March 26, 2016. You can travel comfortably from Tokyo to Hakodate by the Shinkansen.
Taking the Hokkaido Shinkansen, Hayabusa, from Tokyo Station, you will arrive at the Shin-Hakodate-Hokuto Station in about 4 hours on the fastest service. From the Shinkansen Station, it takes 15 to 20 minutes to get to Hakodate Station by the new access train Hakodate Liner.

Following upon the advancement of the Shinkansen, a discount ticket called the JR East South Hokkaido Rail Pass has been launched for foreign visitors to Japan. It is a free pass that can be used from Tokyo through the Tohoku area and Hakodate to Sapporo. It is valid for any 6 days of your choice during the 14-day period from the date the pass is issued. It costs 27,000 yen if purchased in Japan, while 26,000 yen if purchased outside of Japan.

==>JR East-South Hokkaido Rail Pass

==>Information about Japan Rail Pass