Akureyri can easily be explored on foot or by bike. A rental bike usually costs around $15-$20 per day. If you're visiting in winter month, it's recommended to rent a car since the area can be slippery and snowy. You should budget for additional $50-$100 for transportation costs.
If you have more time, consider taking a day trip to nearby attractions like Lake Mývatn or Dettifoss Waterfall. If you have less time, you might want to consider skipping the Botanical Garden and the Folk and Outsider Art Museum.