Near the Guggenheim there are several EXPENSIVE hotels, the Sheraton, the Miro, Lopez de Haro and the Domine.
But just a little further you have other hotels that are not so expensive: Barcelo Nervion, Hesperia.
BUT, if you need really CHEAP hotels, try hotel Estadio (Av. Zunzunegui, San Mames stadium area). It's not so far, in fact it's a walkable distance, but if you don't want to walk you have a tram stop in the door that will leave you in front of the Guggy in a matter of minutes.
Need info about Bilbao? ask me!