The ancient if modest Urgelling Gompa, a 3km walk below Tawang town, is where the sixth Dalai Lama, a Monpa, was born in 1683. Before he left for Lhasa, it's said that he stuck his walking stick into the ground just inside the monastery gate and it eventually grew into a giant oak tree. Within the main hall are hand-painted portraits of all the Dalai Lamas, and imprints of the forehead and feet of the sixth Dalai Lama.
The gompa is 6km from town if you go by road. Note that it's often closed, and if the caretaker isn't around you'll only be able to enter a small side hall with nine chortens.