In the area around Krýsuvik on the Reykjanes peninsula, there are several geothermal areas and springs tied together by foot paths. The area seems interesting for hiking (along the path; with springs at 80-100 degrees C, you don't want to accidentally step on a thin crust that breaks into a mud pool!).
Austurengjar is a geothermal area extending from east of Lake Grænavatn to Lake Kleifarvatn in the north. The hot springs, mud pots, and fumaroles are scattered over a fairly large area, but if you have time and want an interesting hike it could be added to the itinerary. Austurengjahver is the largest hot spring in this area. It is reached by a 1,6 km walk along a seemingly forgotten, sometimes faint but sufficiently marked trail.