Iceland is a great place (I was an exchange student there, and occasionally go back) There's a lot of history and lots and lots wonderful nature. And hot springs.It doesn't have the same amount of show off viking-age history as Denmark/Sweden/Norway, but I recommend the The National Museum of Iceland - Þjóðminjasafn Íslands & The Settlement Exhibition 871 - Landnámssýningin. I've heard okay things about Árbær Open Air Museum - Árbæjarsafn as well. My absolute favourite is the Culture House - Safnahúsið http://www.whygoiceland.com/culture-house-museum-in-reykjavik.html, which house the some wonderful mediaeval manuscripts (which is what I like, I must admit), I recommend the guided tour.As for other things:As has been said, read the Sagas (or a synopsis thereof) and take a tour looking for the places talked about there (tehre are a couple of them offered). And if you do the golden circle tour you get to see the Þingvellir.BUT, what I love the most about Iceland is a) the natureb) the poolsc) pretending to be cool in ReykjavikI really really recomend looking at the nature, and if you're thus inclined, go hiking (although do not be a studid foreign tourist, read & heed the warnings! (Or join an organised tour)). You can go watch volcanoes and glaciers - all in the same tour. It's just amazing.And go to the pools! http://www.swimminginiceland.com/ Not just the Blue Lagoon, but the local pools, there are seven in Reykjavik alone, and they cost less than a caffe latte at the coffee shop. My "local" used to be Vesturbæjarlaug, but all of them are recommended (another favourite is Sundhöllin). And if you want to combine thermal pools with nature - get thee to Landmannalaugar! http://www.landmannalaugar.info/And when you are exhausted and suitably clean, you can hit the town in Reykjavik. It is a small town, but there are al lot fo tourists of all sorts, which makes for variety (although sometimes expensive).So, don't hesitate - go! Bring warm and waterproof clothing!