Comradebirch,
Here are some links for Quebec City; the first is for the youth hostel in the heart of Old Quebec, the second is the government's tourism page.
Auberge international de Québec :
www.cisq.org/en/index.html
Quebec government official tourism website with accomodation database :
www.tourisme.gouv.qc.ca/anglais/index.html
Enjoy your trip !