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.