To leave Tamchy, wait by the side of the main road and hail down cars. If you see a minibus stopping, ask where they are going and if they have room for you. Many minibuses pass through so this should be fairly easy to do. Cholpon-Ata is 45 km away, Karakol 180 km, Balychy 48 km, and Bishkek is 220 km.
