Brennisteinsalda (Sulfur hill) is a small mountain/volcano, approximately 800 meters high. On most days, standing at its top gives you a great view of Landmannalaugar and its surroundings, and even a good look at the Icelandic Highlands.
From the service center, since you are already at 600 meters, the elevation is only about 200 meters. The first half of the hike is the same as that of Laugahringur, but instead of turning left or east by the smoking sulfur rocks, you have to continue upwards. The path through the lava steps is a bit steep and narrow, but it grows relatively easy once you are on the yellow gravel path near the top.
The hike from the service center Landmannalaugar to the top of Brennisteinsalda is approximately five and a half kilometers. So, you should prepare yourself to walk eleven kilometers. This will take about two and a half to three and a half hours.