Yes, it is safe to drink the tap water and 95% of all water in Iceland comes from springs. It is in fact one of the cleanest and most delicious drinking water in the world.
HI Iceland
Vagnsstaðir HI Hostel
Reykjavík - Dalur HI Hostel
Sæberg HI Hostel
Reykhólar HI Hostel
Berunes HI Hostel
Seyðisfjörður HI hostel- Hafaldan Old hospital
Kópasker HI Hostel
Korpudalur HI Hostel
Vík HI Hostel
Reykjavík - Loft HI Hostel
Skyrhúsið HI Hostel
Eyrarbakki HI Hostel
Grundarfjörður HI Hostel
Broddanes HI Hostel
Dalvík - Gimli HI Hostel
Höfn HI Hostel
Húsey HI Hostel
Fljótsdalur HI Hostel
Check the top secret recommendations from the staff