This threesome, considered to be our greatest tourist attraction, is known as The Golden Circle and they are located east of Reykjavík, Þingvellir (Thingvellir) nearest at about 40km.

Þingvellir 
Þingvellir (Thingvellir, 'plains of parliament') has a lot going for it; it has a scenery which is among the most captivating in Iceland, it is the most historical site in Iceland and has very special geological assets. Also, it's located only 40km or so east of the capital Reykjavík.

Þingvellir became Iceland's first þjóðgarður ('national park') back in 1928. It was there that Alþingi was founded and operated from 930 until 1271 when Icelanders submitted themselves under the Norwegian king. The alþingi was still operated but under a different system until 1798. Since 1843 Alþingi has been located in Reykjavík.

Interesting locations: Almannagjá is the greatest rift in the park and a must to see. The location where the goðar(parliament leaders) had their quarters while at Þingvellir is known as Búðir ('booths') and remains of some of the quarters can still be seen there. Þingvallakirkja is an old wooden church that is worth a look. One of its 3 bells dates back to 1698. Lögberg ('Law Rock') is where the lawspeaker cited the laws annually (1/3 of the law books each year). Drekkingarhylur has a bit morbid history; Under laws which passed in 1564 all women that were found guilty of infanticide, adultery, perjury or any other criminal act would be executed by drowning. The drownings took place in that pool which soon became known as 'drowning pool'. Icelandic men who were executed were usually beheaded or hanged.

The largest lake in Iceland is located at Þingvellir and fittingly named Þingvallarvatn ('lake of plains of parliament').

Getting There: There are trips between Reykjavík and Þingvellir once or twice a day from June 1 until September 15. These trips include only very short (30 min or so) stops at Þingvellir (usually using Almannagjá as a base of operations) so you might want to get there by other means.
 
Gullfoss
Gullfoss ('Golden Falls') may be the star among tourist locations in Iceland, but it was not always so as the Geysir area only 10km west of Gullfoss had it completely overshadowed until this century. This is where the massive river Hvítá ('White river') dumps its water 32 meters into the 70-meter deep and 2.5 km long canyon below resulting in an extremely beautiful waterfall.

During the middle of this century this site was almost sold to foreigners for hydroelectric development but a nearby farmer, Tómas, and his daughter, Sigríður Tómasdóttir, successfully lobbied against it. Sigríður walked all the way to Reykjavík to save the waterfall and even threatened to throw herself into the waterfall would it be destroyed. The government then bought the site and set it aside as a national monument. There is now a monument to Sigríður above Gullfoss.

Getting there: The daily bus to Gullfoss and Geysir from Reykjavík passes through Laugardalur instead of Biskupstungur.

Geysir
 While at the Geysir area you will see Geysir's smaller brother, Strokkur, blow burning hot water about 20 meter high into the sky. This he does at about 3 minute intervals and thus serves as a sort of monument of how Geysir himself used to be before it was damaged almost beyond repair by tourist earlier this century which threw rocks and dirt into Geysir in an attempt to set it off.

The great Geysir himself (who could manage up to 80 meter high strokes) can these days only be seen on June 17 [Independence Day] when tonnes of soap are poured into it resulting in maybe 60 meter high bursts. (I am not sure we still do this though).