For Friday and Saturday night the cheapest way is to sleep on the floor of a reserved non-smoking room. You only have to bring your sleeping bag and air mattress.
You can also bring your tent and just camp on the area.
The Auryn team provides a cheap breakfast for you.
If you want a more comfortable way to sleep you find here all hotels in Stuttgart/Böblingen: Link to hotels (German website - contact us if you need help)
The closest, but not cheapest hotel is:
“Hotel-Restaurant Böblinger Haus”
Keilbergstraße 2 - 4, 71032 Böblingen
Telefon 0 70 31/2 11-0, Telefax 0 70 31/22 98 11