While in Reykjavik, go to Hertz and rent a car and buy the audio tour for the Golden Circle. IT takes about 4-6 hours, but it is a great drive through the country. Youll see some freat waterfalls, geysirs, lakes, horses, killer sheep, and more.
At night, be sure to check out
Kaffibarinn , people might tell you the Damon Albarn, but last time I was there I was told that was just a rumor that was spread to get people in the door. Still a cool place though.
Also check out Sirkus. Great bar, but get there early as the line goes down the block to get in past 2am.
For a good meal try Vegamot. Also has a good nightlife.
For shows, try Nasa, Gaukurinn, Grand Rokk.
Are you staying in Reykjavik? or by the airport? There is a 45 minute bus ride from the airport to the city. Get the bus right outside of baggage claim.
Another cool thing to do is to go to the Blue Lagoon (large hot spring) at night. Some nights you can see the Northerrn Lights, but we weren't so lucky.
Iceland is fun, but expensive...Bring a Visa or Mastercard, NOWHERE took AMEX.