Pfaffenhof 1 and Pfaffenhof 2
Although hostel Pfaffenhof I is one of the oldest hostels in Stuttgart, it is one of the prettiest and best equipped since the renovation in 2001.
The hostel Pfaffenhof II is a really nice hostel too and was completed in autumn 1996.
The boxy architecture seems to be somehow unusual but provides lots of rooms and appartments in Pfaffenhof I as well as living communities of 4 students in Pfaffenhof II.
As they belong to the Studentenwerk Stuttgart, there are many services provided by volunteers, you can look up on this website.
The hostels are situated between the university in Stuttgart-Vaihingen and a natural reserve. You can reach the S-Bahn in around 5 minutes on foot and by this you can reach the city within 10minutes.