Hachinohe (八戸) [1], a mid sized city in Aomori, is the current terminus of the Tohoku Shinkansen line and mainly a train hub for most travellers.
Hayate trains from Tokyo reach Hachinohe in three hours and cost ¥15350 each way, so it might be wise to get a rail pass of some kind before making the journey.
Hachinohe has an extensive train and bus system, all using the same station as the bullet train.