Trashigang (population 4,500) is in an administrative town in the east of Bhutan. The traditional architecture and narrow streets give the town a quaint and snug feel, not unlike an Italian or Cornish fishing village.
From Thimphu there are two routes, both requiring two days: On the northern route there are direct buses that make a night stop at Jakar and pass through Mongar. The southern route passes through Phuentsholing, where you'll need to arrange private transportation to Samdrup Jongkhar as there are no buses on this route. This leg of the journey passes through the Indian states of West Bengal and Assam. From Samdrup Jongkhar, there are direct buses to Trashigang.