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the city is very small and can easily be walked avoiding . Buses through the generally very city are free, but only come once an hour. Buses to the surrounding country side are quite expensive local transport, as are all public transports in Iceland. 

Walk towards to the national road n^1 (ring road of the island) on the northeastern part of the city. You'll easily find proper traffic lights and roundabout roundabouts more than adequate to start hitchin. If you are carrying a lot, you can also take the free bus line number 1 to Miðsíða. This is the farthest out of Akureyri and the closest to the ring road you get by bus.There you can stand right after the roundabout in direction Reykjavík.