Central Akureyri is quite compact and easy to get around on foot. If you plan to park a car in the town centre you'll need to get a parking clock (free) from the tourist office, banks or gas stations.
At the time of research there was nowhere to hire bikes in Akureyri, but ask at the tourist office, in case the situation has changed.
There’s a free town bus service on six routes, running regularly from 7am to 8pm weekdays and 1pm to 6pm weekends – look for the yellow buses. No route serves the airport. The tourist office has a printed bus map and schedule.
Akureyri has a unique parking system for Iceland (one that many northern Europeans will be familiar with). When parking in the town centre, you must set a plastic parking clock indicating the time you parked, and display it on the dashboard of your car (so as to be seen through the windshield).
Parking is free, but spaces are signposted with maximum parking times (from 15 minutes to two hours, enforced from 10am to 4pm weekdays). Note: '1 klst' means one hour. You’ll be fined if your car overstays the advertised time limit. Pick up a parking clock (free) at the tourist office, banks and petrol stations.