The DJH youth hostel in Mainz is very nice and modern as well.
Prices are about 24EUR/night for a single room with toilet and shower. Sheets and towels are included, as is breakfast. Lunch and dinner add-ons are also available. I believe the hostel has wireless internet for a fee. You do need to have a hostel membership or purchase a guest card at the hostel (ca. 3EUR/night).
http://www.diejugendherbergen.de/cms...dcat=256&LN=en