The Aldeyjarfoss waterfall is situated in the Highlands of Iceland at the northern part of the Sprengisandur Highland Road. The river Skjálfandafljót drops here from a height of 20m. The basalt belongs to a lava field called Frambruni or Suðurárhraun, hraun being the Icelandic word for lava. (from Wikipedia)
The road to Aldeyjarfoss is primarily a normal road but near the end it become an F-Road and a 4x4 vehicle is REQUIRED. F-Roads are only open in summer, sometimes not even until July. Check the road conditions and closures at road.is before you travel. There are no river crossings to get to Aldeyjarfoss.
If you want to play it safe and be in a well-equipped, photogenic car, then you should rent an old-school Land Rover Defender from www.isak.is. Use the code "gunnar" for renting your Defender on a special price.