Another vote for the Golden Circle and Blue Lagoon. I don't know whether it's best to do it by rental car or an organised tour... I drove a car in Iceland and I found the roads are easy (there simply aren't many) and even the free "Big Map" you can pick up at the airport is detailed enough to find Geysir and Gulfoss and Thingvellir, and your way around Reykjavik.
Most car rental companies allow you to pick up or bring back the car at the airport or in Reykjavik (at your hotel), it doesn't matter... for example they bring the car to your hotel, but when you're done you can leave it at the airport, or the other way around, or you do both the picking up and the returning at the airport (or hotel). I had an okay price through Sixt and they gave very good service.
Usually you can also opt for renting a navigation system to go with the car. But I was fine without one.
Using your own transportation will allow you to stay as long as you want at each of the sites. But if you don't want the hassle of renting a car and finding your way then a tour might be easier.
I really loved the Strokkur geyser and all the other hot spring type of things at the Geysir site, and stayed there for at least an hour. I also loved staring at the Gulfoss waterfall from various points.
Blue Lagoon could be nice for the evening if they're still open late... soak in a hot spring under a starry sky... take off all your jewellery or it will turn black! ... or go there just before you fly.
Reykjavik itself is small and you don't need a lot of time there. I don't know if "the Vulcano Show" features at night but it could be a nice way to pass a few hours after dark watching amazing footage of vulcanoes going off or even forming entire new islands of Iceland's coast.
Have fun! Iceland-specific tips on my website under Travel > Iceland 2007.
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