We recommend that you stay at Hotel Føroyar: www.hotel.fo
This hotel is situated in a very nice area, and close to the where the competitions will be held.
The Hotel also has a hostel - Kerjalon - available, which is also situated in the same place as the hotel.
or Torshavn tourism agency: http://www.visittorshavn.fo/
Another hostel has: www.hostel.fo