To mention few :

Sightseeing tours in the neighbourhood

Hiking tours suitable for everybody, for example to Hellisfjall, Mount Loðmundur or Sáta

Looking for caves in Hellisfjall

Lava field hiking in Lambafitjahraun

Observing the huge contrasts in nature

And at last but not least enjoy the overwhelming silence and peace

It is also popular to organize parties in the old sheep gatherers' hut and sing there and tell amusing stories.