The key to really learning Reykjavik is the stopover
If you go somewhere as exotic as Iceland -- or as exotic as Indianapolis, for that matter -- you really need to tap a local to get these kinds of insights. For as strange as Iceland is, it’s also small-town friendly, and residents would like you to stop by. Their economy increasingly depends on visitors: Last year, for the first time, American tourists arrived in numbers (350,000ish) that surpassed the country’s population. Iceland has only about as many people as Tulsa, and remains lonely at sea between Scotland and Greenland. Frankly, they seem to enjoy seeing new faces.
Head over before spring, and there’s an easy way to make friends while you’re around. Icelandair is running a promotion at least till the end of March wherein you may request what the airline calls "Celebration Stopover Buddy" service, and they’ll set you up for a day with one of their employees. Essentially you get to borrow a regular Icelander: tour guide, chauffeur, cultural ambassador, shark procurer. You have to cover any expenses you rack up (the buddies get reimbursed for theirs) but, regardless, you can't do much better than your own local for a day who's super amped to hang out with you. One of mine, a programmer named Óttar Guðmundsson, showed me phone pics of the day he took out a couple celebrating an anniversary. Dude surprised them with balloons and a cake in his dang trunk.