Iceland is among the northernmost places that we visited. The walking tour guide in Reykjavik told us that the guy who discovered it didn't want anyone else coming over for competition and called the place 'Iceland'. He also took the much larger chunk of ice to the west and called that Greenland to maximize misdirection and confusion!
In reality, there is a lot more than just ice in Iceland. It has stunning natural landscapes and is dotted with beautiful waterfalls, geysers, beaches and a rough, wild landscape that is a delight to drive through and wander about. And then, there are the wonderful Icelandic horses.
The population of Iceland is about 365,000. In comparison, the least populated state in the United States is Wyoming and Wyoming has about 550,000 residents. There is one international airport: Keflavik (KEF) just outside the capital city of Reykjavik. The Capital Region (in and around Reykjavik) which is in the southwestern corner of the island contains almost 2/3rds of the country's population. This means that if you are willing to drive a little out of the way, you have the country almost entirely to yourself.
Before you strike out on the highway too far from town, remember that the number one attraction of Iceland is the Blue Lagoon which is a geothermal spa not far from KEF. In fact, it is close enough that many people with a multi-hour layover can sneak a trip there and back from the airport. The water in the blue lagoon gets its color from the high silica content but once inside the pool, it doesn't feel any different - except it is warm and toasty when outside it can be really chilly. It's definitely worth a trip even if it isn't cheap.
Reykjavik itself is a pretty small and compact city. There's not a huge list of things to see here except the striking lutheran church Hallgrimskirkja and the Harpa, which is Iceland's national concert hall.
There are two loops that visitors can take. One is a circumnavigation of the entire island which can typically take a week or ten days. A smaller loop is the famous Golden Circle than often takes 2-3 days to cover and that is what we ended up doing. There is lots to see on the Golden Circle. Once you get out of this area and head into a circumnavigation you had better plan well because you are going to be in very very sparsely populated country. But it's beautiful so a circumnavigation is definitely something to consider if you have the time.
The other thing to consider is a summer vs a winter trip. The famous Northern Lights or Aurora Borealis are a definite possibility in Iceland but only in the winter. The downside of Icelandic winters (in addtion to the bitter cold) is the few hours of sunlight - twilight really. Just remember to brace for 20 hrs of darkness when you go to chase the Northern Lights. Our summer trip on the other hand meant we didn't have a chance at the Northern Lights but we did have 20 odd hours of sunlight. And even midnight is only a gentle twilight. One can still read newspapers at midnight or 1 am on the street. Which we did even if it was an extremely toursity thing to do. But it was quite the experience to have a late dinner and then head out for a drive and have perfect visibility at 10 pm and walk around at midnight as if it were late afternoon!
Iceland abounds with waterfalls. The icelandic word for waterfalls is foss and it seems like you can't drive far without coming across one. Some of the best known ones are Goðafoss ('God' waterfalls), Seljalandsfoss where you can get behind the curtain of water, Skógafoss and Gullfoss.