Yes, there are craft breweries in Iceland. There aren't that many, but with a population of only 300,000 people that's to be expected. The main ones are Einstök, Borg, Gædingur, and Ölvisholt. There's also Stedji and Kaldi, but these are less interesting. I felt Gædingur was a bit variable on quality. Note that none of these produce extreme beers. They focus more on drinkability.
Only Borg is in Reykjavik. I don't know if you can visit the brewery.
You can't buy interesting beer in Icelandic supermarkets, because the alcohol limit is 2.25%. As far as I could tell, only 4 beers were available in supermarkets, all of them pale lagers. You have to go to Vinbudin. There's a branch in the Austurstræti in the city centre, but the one out in the Kringlan shopping center has a bigger selection.
Look for these bars in the Reykjavik city centre: Micro Bar, Cafe Laundromat, K-Bar, and 73. All of them on Austurstræti and Laugarvegur.
Edit: I forgot to say what's the most unique/distinct beer. I'd say Borg Fenrir, which they describe "tadreyktur IPA", meaning IPA smoked in the traditional Icelandic way. That is, it's smoked by burning sheep dung. (Seriously.) The smoke aroma is really unusual, but actually quite nice.