This is c.a. one and a half hour drive. You should begin on the south part of the rout. Shortly after the beginning there is a straight and not very interesting road heading to the mountains where suddenly the road begins to be very interesting with lot of curves and great and beautiful landscape. You should be aware of that most often the road surface is, although it is asphalt, with sand, loose rocks and holes that can be very dangerous so it is important to read the corners very well before you lean into them. Behind the mountains you get a beautiful view over the naitonalpark Thingvellir which is if you want to lengthen the trip, worth the visit.
This is a beautiful few houre drive with spectacular view over Hvalfjordur (Fjord of whales). In in the WWII the Fjord was often full of ally ships gathering together for a big convoy for there journey over the Atlantic ocean. At the end of the Fjord you can see the highest waterfall in Iceland called Glymur. On this route there are plenty of interesting places to stop at and take a closer look at.