Graz doesn't have too many cheap accommodations. I was here for only two nights, so I booked my bed before I arrived. I arrived at the Hauptbahnhof from Klagenfurt. The Jugendgästehaus is about one kilometer from the Hauptbahnhof, and you find many signposts.
This is a very large, purpose-built accommodation and is used for school groups as well as independent travellers. Conferences take place here also. There is a reception, café and bar, and you can use the Internet here. Also, you can do laundry. There is a large dormitory in the basement and also rooms to sleep four persons.
My bed was in a four-bed room, but I was the only person both of the nights. It was on the second floor and looked out to the front of the building. In the room, there is a bathroom with shower, toilet, and washbasins. I had also a television in the room. On each floor, there is a common room area and drink machine.
The price of accommodation changes. It is cheaper when you have a youth hostel card and also when you stay more than four nights. You must pay a supplement when you stay less than four nights. I paid €25 each night, but that included breakfast.
Breakfast is from 7 to 9am and is self-service. It is a very good meal for a youth hostel. You can have cereals, toast and breads, fruit, yoghurt, coffee, tea, hot chocolate, and fruit juices. Eat as much as you want.
It is easy to get to the city centre from here; there are many buses and trams, or you can walk. I was coming back late one night, and a taxi from the city centre cost me €6.
There is no home-like atmosphere here--it is too large--but the staff are very friendly, and it is comfortable. If you need to stay somewhere cheap in Graz, I recommend you try here.