I would start following things on FB like the Reykjavik Grapevine and the local music spots such as Húrra, Kaffibarinn, Gaukurinn etc... That way you will find out about concerts and events that are going on while you are there. I know that Soley/Sin Fang/and Orvar are playing June 1st.
I heart Reykjavik is a good travel site done by an Icelander, and they also do tours around the city, and of course I always recommend on tour with ívar, he's in FM Belfast and gives an excellent walking tour of little known places around the city. It's the spendy one, but you do get food, cocktails, and stories.
And personal opinion and such, I would definitely check out Messinn in Iceland for the Plokfiskur (fish stew). Even the locals say it's the best in town. And find Fischer, it's a great little store and they have a 7" soundtrack with Jonsi inspired/curated/created stuffs on it.