Here are The Traveling Professor's picks of the best things to do in Iceland:
Blue Lagoon: I used to think this was too touristy for me but it really is enjoyable. The crowds are controlled, so there isn't too much of a problem with too many people enjoying the Blue Lagoon. However, that means reservations should be made well in advance.
Golden Circle Tour: This is an excellent introduction to Iceland. It takes about 6-8 hours to see the geysers, gigantic waterfalls, and natural beauty of Iceland. I recommend a private tour.
South Coast Tour: Don't miss this one if you love volcanoes, black sand beaches, stunning scenery, waterfalls, and if you're lucky some puffins. It's a long day out from Reykjavik and again, we recommend a private tour.
City Walk: There are a variety of city walks available in Reykjavik. It's always good to get an hour or two tour of the city.
Bonus Seasonal Activities: The Northern Lights go on from about October to March and in the summer, try a whale-watching tour.
Check out The Traveling Professor's small group tours to Iceland: http://travelingprofessor.com/Tours/NorthernLightsofIceland.aspx