Most people who visit tend to go on the Golden Circle tour which will take you to see the huge crack in the earth where the tectonic plates from North America and Europe meet underneath iceland at Þingvellir (first the first parliament was also established). The route also includes a visit to the geysir, where hot spings sprout out water fairly regularly as well as the enormous gulfoss (huge waterfall) nearby. This should only take one day.Some of the options are  Golden Circle Bus and Super Jeep Tours, and Golden Circle Minibus Tour.

A trip to Iceland is not complete without a trip to the Blue Lagoon. It is a geothermal hot spring which feels like you are in the most soothing bath of your life. It is said to have healing properties too. Bathing at thermal springs is a very popular custom in Iceland. It may be nice to go at a time when the sun/light is available and towards the evening time as it is really magical to see it during both daylight and nighttime as the water is iridescent blue. http://www.tour.is/day-tours/the_blue...

Also recommended is the sea boat tour on the glacial lagoon at Jokulsarlon which was just stunning. It is a must do if you have the time. It is further to get to but worth the trip. The drive takes 5-6 hours to get there so you may need to stay overnight close to the area.  You can buy tickets for the boat trip at the site, the tour takes 40 mins but you actually get to cruise with the icebergs around you. The lagoon connects to the beach which has black sand due to the volcanic activity. The tours may not be open all year round so check first: http://iceland.vefur.is/Iceland_trave...  

Iceland has come under much international scrutiny and pressure for its whale hunting. However there is now more focus on capitalising on the tourism opportunities with whale watching tour operators. You can buy the tickets on the day at the wharf just before the boats take off. You can also get the opportunity to see the very cute puffin colony. http://www.elding.is/tolbar/whale_wat...  

There is also the opportunity to do something different like go on a glacial hike also which was good fun. There are two main glaciers there so you can chose whichever suits you.  http://www.adventures.is/Iceland/Glac...  

It is worth spending a day in Reykjavik as well. It is a really lovely town with cosy cafes and friendly waiters and shopkeepers. There is a beautiful church at the top of the hill that you can't miss. You can take a lift to the top for a spectacular view of the town. At the other end of town (which isn't all that far really, you can walk the whole town quite easily) there is a lake where the ducks feed. There is a building right on the lake which is really worth visiting as you get to see a model of the country, there is usually an exhibition going on and there is also a lovely cafe.  

Places to eat: Nonnabita (try the lamb subs), Hotdogs (the best one is at the outdoor stand near the carpark near the indoor flea market). Definitely go to VOX at the Hilton hotel on the weekends for the buffet. It was great value (a huge range of seafood, lamb etc pls desserts!). Perlan is a beautiful building which has wonderful city views and a lovely restaurant for a special occassion or just hang out at the cafe for a hot coffee. Tiu Dropper is also a quaint coffee house on the main street but there are plenty of cosy cafes to just sit back and relax.