Two very cheap options for those staying in Bilbao: http://albergue.bilbao.net/ing/introing.html and http://www.bilbaoakelarrehostel.com/ing/site/albergue.asp (direct link to the English version). As Bilbao is a walkable town and with an excellent transport system, distances to the centre and main places are not an issue. Both on very safe neighbourhoods (Bilbao is, in any case, extremely safe). Prices are simply unbelievable (breakfast included) and both places are inmaculate clean. For all ages, although they are mainly used by young people.
Hostel Accommodation in Bilbao30 11 2009