Oxararfoss (or more accurately Öxarárfoss; I think is pronounced "UEWX-ar-our-foss"; meaning "Axe Falls") was a waterfall that seemed to be more of a side attraction in the historically important UNESCO World Heritage Site of Þingvellir ("THING-vet-lur"). Moreover, I believe this was actually an artificially created (man-made, if you will) waterfall due to water diversion that took place several centuries ago to provide better access to drinking water for the assemblies or Þing (pronounced "THING"). I'm still a little fuzzy about the validity of the statement about water diversion, but apparently it's said that there is geological evidence of an old riverbed west of the river's current location.
The assemblies were important for Iceland's eventual independence because this was where consensus decisions were made. The water diversion might have also created a drowning pool (Drekkingarhylur), which we were able to see while touring the area. It's said that the pool was used to drown women accused of infanticide, adultery, or other crimes.
Given the historically significant nature of Þingvellir, it was fitting that we also learned there was a saga related to how the waterfall and river (Öxará) got their names. Apparently during the settlement period in Iceland's early human history, some settlers encountered a frozen river. They then dug a hole in the ice and put an axe in it to claim the land. The word öxi means "axe" in Icelandic.
Regardless of its origins, we found this to be an attractive waterfall (said to be 20m tall) and gave us the waterfaller's excuse to visit Þingvellir. As if that wasn't enough, this area also happened to be in a rift valley where Iceland is getting pulled apart by the Mid-Atlantic rift between the European Plate and the North American Plate. The volcanic cliffs attesting to the fiery past of this region provided some interesting geology as well as atmosphere to our visit.
The falls was located on the eastern end of the rocky fault line. Although an out-and-back visit to the falls would probably take an hour or so, we spent nearly two hours here just so we could visit the other sights (like the Law Rock or Lögberg, the drowning pool, and the vistas).
Since we happened to show up late in the afternoon, we learned that this east-facing waterfall was against the sun. We actually waited for the sun to sink behind the cliff containing the falls to get the photos you see on this page, but I'd imagine that the best color and light would probably be in the morning.
Directions: Þingvellir is one of the major attractions on the Golden Circle and is about 54km east of Reykjavik via the shortest approach from the west (along Route 1 to Route 36 to Route 361 and finally Route 362).
We parked at a car park for the Law Rock, but there was a separate car park at the trailhead for Oxararfoss just a few minutes of walking further to the northeast.
If you're coming from Geysir (or Gullfoss), you can take the road 35 west to road 37. Then follow the 37 to the 365, then turn right onto the 36 before taking the 361 towards its junction to the 362.
Since we made our visit from Faxi, we followed the route 35 west to the route 36. Then, we took the 36 north to the 361 and ultimately the 362 (a total of about 61km of driving).