By car or bus
The city is linked to the rest of Iceland via the Ring Road, the highway that circles the island along the coastline. Busses between Reykjavík and Akureyri are operated by Sterna , while busses from Egilsstaðir and various other towns to the east of Akureyri are operated by SBA .
Akureyri has an airport with flights to and from Reykjavik Airport on domestic carrier Air Iceland  several times a day. Air Iceland also has flights from Akureyri to three smaller villages: Grímsey (a small island to the north of Iceland, on the arctic circle), Þórshöfn (in the northeast on Langanes peninsula) and Vopnafjörður (the northernmost fjord in East Iceland).
Being Iceland's northern capital doesn't mean Akureyri is a huge metropolis. Although it can get a bit hilly leaving the waterline, walking distances are reasonable for a fit traveller.
Akureyri has a public bus system, called SVA, which is free for all. The bus schedule is not very frequent, with one bush every hour or so on each line and the busses stop running at 11pm on weekdays and only run between 12 and 6pm on weekends and holidays, but when they're for free why complain?
BSÓ  is the only taxi company in town, and they have a taxi rank in the centre of town.
Akureyri is a very picturesque town with its location by a scenic fjord, eclectic building styles and streets winding their way through gorges. Spend some time walking around the town centre, see the impressive church and check out Listagilið (literally: "the art canyon"), home to a number of arts and crafts galleries and shops. The tranquil municipal botanical garden, Lystigarðurinn , is worth visiting, as are the several small museums dotted around town.
Typical of Icelandic cities, there is a heated outdoor pool and hot-pots available to the public. Thorough showering before and after bathing or swimming is expected.
A local way to eat a hamburger is with french fries included in the bun and kokteilsósa (a cocktail of mayonnaise and ketchup). A shop that sells a delicious version of this called a MacGratsky burger is Nætursalan located downtown right next to the main bus stop. This is a popular snack to end the evening after a heavy night of drinking. Akureyri also has the world's northernmost Domino's Pizza. Rub23, located just below the cathedral of Akureyri, has a most friendly atomosphere and serves one of the best fish dishes in the area.
The Indian Curry Hut, located at Hafnarstraeti 100b, has some of the best curry in all of Iceland--perfect for warming up after a winter's day! It's a take-away, though there are two stools and a counter. The owner of the restaurant is very friendly, with an interesting life's story.
Strikid: Fresh, high quality restaurant. Their chocolate cake is the best I've ever had, hands down. Mostly fish, lobster, but one or two meat dishes. Has an amazing view at the top floor of a building at the coastline. Greifinn: Considered high quality, just sells sandwhiches, starters, soups. Obviously a nice restaurant though.
A nice bar is across the street from the main movie threater. It seems that people in the city enjoy an 'early' movie theater around 8pm or so, and, as customary in Iceland, go clubbing/barhopping after midnight. However, the clubs close at 1AM, at least during the weekdays. A strange wheel-of-fortune with shots, beer, and nothing, is there, for 1500 Kr.
There are many guesthouses more inland immediately away from the city center. They double as residences for college students, but they are the cheapest lodging you'll find, at around 8000 Kr double and 5000 single.
Akureyri is a good base to explore some of the more remote areas of Iceland, such as Mývatn. Several buses run mostly hourly from the city centre to other important places like the airport and neighbouring settlements and bus tours are available which take you to see the enormous crater of Víti, and Goðafoss (waterfall of the gods).