If you want to go for real bargains regarding your accomodation, we recommend consulting the following specially compiled list of budget accomodation options in Graz here.
Please note that they have only limited capacity and available beds will quickly sell. Bookings have to be made individually by contacting the listed hostels directly.
Simple bed&breakfasts as well as private accomodation can be found at Graz Tourismus and at well-known homestay marketplaces. You can also search the full range of other accomodation options in Graz which are available online via this site.
If you prefer a higher accomodation standard, please consult the general accomodation offers.