There are no hostels in Stokkseyri but there are other types of accommodations...

"We offer budget accomodation that is clean, comfortable and with friendly and helpful service of our staff.
Accommodation is in beds, in 2 - 6 bedded rooms. There are duvets and pillows in the beds and bed linen can be hired at a small cost. Guest may cook their own meals without extra payment."
From Airport Keflavik which is about 80km away from the GuesthouseYou can take a bus from the airport directly or Guesthouse South will arrange Airport Pickup
Gistiheimili Suðurlands,...

"We offer budget accommodation that is clean, comfortable and with friendly and helpful service of our staff.
Accommodation is in beds, in 2 - 6 bedded rooms. There are duvets and pillows in the beds and bed linen can be hired at a small cost.
Guest may cook their own meals without extra payment.
In between Selfoss and Eyrarbakki - excellent location for daytrips to Reykjavík, Þingvelling, Geysir, Gullfoss, Reynisdrangar, Hveragerði, and Vestmannaeyjar ect."
The Bus stop is in...