My favourites are the Blue Lagoon and Thingvieller (sp?), and the glacier. Also go to hot springs area ("geyser" is an Icelandic word).
Here's a suggestion: Get a copy of "Niall's Saga" to read before you go. The Icelandic sagas are the stories of their history through many generations. It's huge, but I ended up reading it from cover to cover. I strangely found it both informative and hilarious. It's not intended to be hilarious, but man, I thought it was. It talks about the biennial meetings at the Thingvieller where all the legal battles are decided with lawyers and judges (e.g., because Lars killed Thor's cousin over a battle about a goat, Lars arguing it was an honour killing, etc. Everything always gets settled, and then nobody pays the least attention to the settlement.)
Icelanders are really friendly, somewhat naive folks (very pleasantly so). True story from our visit there about 18 years ago: We go into a bar to get something to eat fairly early in the evening. Only one other table occupied, and it's full of "blue collar" workers, but who are wearing kind of rough tweed jackets and ties (they look like they are in working clothes from the 1920's or something). So there are about eight of them at this table and we are about 12 feet away at a different table. I see a bunch of newspapers in an adjoining room and I go over to see if any are in English so that I can maybe see how the Mets are doing. I'm shuffling through the papers and turn around and one of the guys from the other table is talking to Moms Skillethead, who, I might offer, is attractive and very vivacious.
So, I come back to the table and after a pleasantry, the guy heads back to his table. No problem. Two minutes later, he comes back and apologizes to us for having spoken to my wife without me being there. Three minutes later, one of the other guys comes over to our table and says, "I have been selected from our group to come over and more formally apologize to you for the behaviour of our colleague. It was not right for him to talk to your wife with you not being present. We all agree that this was not the polite thing to do and we are all very sorry." So we tell him it's OK, and then strike up a conversation. He tells us that he lives on an island just off the coast and that we should join him and his wife for dinner before we leave Iceland. Guy is as friendly and earnest a guy you'd ever want to meet. So we take his info (did not take him up on the offer) and go back to our drinks. Two minutes later, the bartender and owner, who has watched all this unfold, comes over so that he can apologize, too. He tells us that these are actually very nice lads and really meant no harm. We have a great meal, and head back to our hotel. We look up the bar in the guide book we have, and it says, "Under no circumstances should you ever go to this bar as it is the most dangerous bar in Reykjavik."
