Hey Vi, would it be too OT here to ask what you'd do in Reykjavik if you only had 2 full days?
No I don't think so. Sorry it took me so long to get back to you, I was out with some friends. Ok so it would largely depend on who you were going with and whether or not you wanted the touristy experience or not.
If it were me, I would say hang out with some Icelanders who really know the area and let them show you their favourite places. Because then you have your own unique experience and you get to see some things that are out of the ordinary. If you are going in winter, you have to see the northern lights, especially if you live in an area where they don't normally appear. If you're going in the summer, stay out late and experience daylight at 2am. It's pretty awesome. If you're renting a car, drive over the speed limit because only tourists drive the speed limit and all the Icelanders will know you are a tourist if you drive the speed limit. If it's not closed for the winter yet, I would recommend climbing Esjan because it's a lot of fun and the view from the top is pretty spectacular. This takes the greater part of a day though. Go get ice cream downtown, go get ice cream at 11pm and witness the phenomenon that is Icelanders queuing for ice cream at 11pm. I know you know a little Icelandic, so try using it. They get so excited when foreigners use their language. If you want to do touristy things you can always go see Geysir and Gullfoss which are the erupting geyser and a waterfall, and Þingvellir national park is on the way. That's cool for two reasons, one you can go see the divide between north america and europe and two that's where Iceland's parliament used to be. If you don't mind driving for a few hours you can go see Jökulsárlón which is a glacial river. If you like art, Laufey took me to see this exhibition of statues in a garden in Reykjavík which is free. The statues are really interesting. I cannot remember the name of the street it's on right now, but I'm sure she could tell you.
Actually you could probably ask Laufey and Steinunn about this as well since they both currently live there. Oh yeah speaking of which, totally go meet Laufey while you're there, because she is awesome to hang out with.