The first stop is Þingvellir (prounounced "Tingvetler") National Park. It is the location where the Eurasian and North American Plate are spreading apart and was the original location of the Alþing, the Icelandic parliament, from 930 to the 18th Century.
The Law Rock, where the laws of Iceland were repeated ever year (1/3 a year - originally they were memorized!).
Next was Gullfoss (Gull Waterfall). 140 cubic meters of water (2800 cubic feet of water) go over the falls every second.
Geysir, where there is an actual geyser:
Friþheimar Farms grows 20% of the tomatoes in Iceland. It a series of greenhouses which uses geothermal energy and CO2 from volcanos to grow tomatoes (and other vegetables).
They are also quite famous for their tomato soup:
Skálholt was (from 1056-1785) one of the most important religious centers in Iceland. It now serves as the national seminary of the Church of Iceland.
Original foundations of the cathedral:
Kerið is a relatively small (and old) explosive volcano crater, now filled with a lake.