There is only one place that counts as a city in Icelandic, and that's Reykjavik. The rest of the population lives in towns.
The Reykjavík area is where 2/3 of the population lives, and therefore where most of the job opportunities are. Some people prefer living in Kópavogur or Hafnarfjörður, but commuting into Reykjavík can be quite slow in the mornings. Same goes for Mosfellsbær.
If you want to live outside the RVK area, Akureyri is a lovely town with great outdoor activity opportunities, especially if you like skiing. With a population around 18 thousand, it's not overflowing with job prospects but there is still decent diversity for such a small country. One disadvantage living there is that if you want to go anywhere abroad, you'll first have to get to Reykjavík where most international flights depart from. Domestic flights are often disrupted in winter due to weather, and the drive is at least 4 hours.
There are several smaller towns sprinkled around the country but I don't know many people living in those places long-term. Usually people who choose to live in those places have family/personal connections that drew them there.