Historically, Thingvellir is a key place to Icelandic. Here was created the first parliament ever, Althing, and in 1940 independance was declared, after several centuries under danish and norvegian dominations.
Geographically, Thingvellir is astride european and american plates. Each year, distance between both sides is growing by 2 cm ! Despite this tectonic activity, the place is very quiet, with tall grass and trees (rare enough in Iceland to be noticed). On top of the american plate, there is a magnificent scenery on Lake Thingvallavatn and Althing buildings. The 30 m overhang is very impressive.
At the very end of Almannaja rift is river Oxara. By leaving Thingvellir to Geysir, you drive across Oxara. If you stop beside the bridge, you can follow the river to Oxarafoss. Then, the river falls into the rift before continuing to Lake Thingvallavatn. The road goes round the rift, then gets on the other side. After climbing a cord lava slope, you discover Oxarafoss under another view.