If you find yourself getting anxious if there is not a bar, place to go dancing, or a wide variety of food options in close proximity at all moments, then it is probably best to just stay in Reykjavik. If you are more interested in art museums and symphonies and shopping from quirky Icelandic designers, then it is also best to stay in Reykjavik. If you prefer to hang out in a cafe drinking coffee and reading, wandering through town, and staying at a modern or chic hotel, then you should also stay in Reykjavik.
Akureyri is almost like a miniature version of Reykjavik, with just a little less of everything and even more small-town vibe. The one big difference is that the landscape surrounding Akureyri is quite different than Reykjavik and is in close proximity to places like the Dimmuborgir lava sculpture garden, the Mývatn Lakes, and Ásbyrgi canyon. So if you felt like Reykjavik was almost your place but you want a little bit more of an outdoors offering, then Akureyri may be your place.
If being a hermit on the arctic circle interests you, then maybe you should visit Raufarhöfn. Located in Northeast Iceland, this tiny village is about as remote as you can get. If you want a secluded place to get deep into your own thoughts, perhaps finish that novel that has been waiting for you to write it for years and years and you want to hear only the whirling arctic wind and bird songs and nothing much else to distract you, then bingo! Go to Raufarhöfn! Also, if being inspired by a Nordic version of the Stonehenge sounds like an inspiring landscape backdrop, then all the more reason to go.
Located in the Westfjörds in Northwest Iceland, Ísafjörður is the largest village in the area. If you like the sound of feeling dwarfed by the immensity of monumentally steep mountains in a place that is nearly inaccessible in wintertime, then Ísafjörður might be the place for you. If you liked the sound of Raufarhörn and thought that might be the place for you but you also feel like you might need to go to a bar and chat with other travellers or hear live music once in a while as you work on your novel, then Ísafjörður could be the place for you.