I had an enjoyable, if bumpy and rather rainy, drive across Kaldidalur in August. This short highland route can be accessed from Þingvellir and driven in an afternoon and will give you a taste of the highlands, including glaciers and the volcano Skjaldbreiður, after which shield volcanoes are named.
Parts of the road were (and generally are) full of holes and in some places the surface is like corrugated iron, requiring either very slow driving, which will take time but give you a good chance to observe the landscape, or driving at around 60 km/h, which will reduce the shaking but requires considerable skill and experience in driving on gravel and so much concentration that you’re liable to miss all the magnificence of the landscape. We call these corrugated iron-like road surfaces “washboards” after the surface of old-fashioned laundry washboards.
The gravel road ends near Húsafell in Borgarfjörður and the blessedly smooth tarmac road down to highway 1 will take you past Barnafossar and Hraunfossar and through the verdant landscapes of Reykholtsdalur and Borgarfjörður.
The cairn is a nice place to stop and look at the desert landscape of the highlands. Just remember to add a rock to the cairn for luck before you leave it.
I never fail to stop at this place when I’m in this area. It’s a place where Hvítá, a glacial river, comes down through a very narrow ravine, almost just a crack, in the rock and you can really see the power in the water as it gushes down the ravine: