Lava tube caves, or volcanic veins, in Iceland are scattered throughout elevations. They were made as the surface hardened, but magma from the volcano continued to flow underground. Be aware of sinkholes when hiking in areas with volcanic tubes, since openings to chambers below are sometimes concealed by heavy moss and vegetation.
Depending on how much time is available and how far one is willing to drive, you can also visit nearby hot springs, geysers, glaciers, glacier lakes, go inside a volcano, and see Gulfoss or Golden Falls. Many points of interest are unmarked, but are accessible for free exploration.