There's a hostel about 1km from Frankfurt Hauptbahnhof, and it's in Hostelling International, which has a good reputation. i haven't stayed at that one (have only stayed at hostels in Geneva, Los Angeles and Honolulu) but a bed in a bunkroom might be as little as 20 Euros.

http://www.hihostels.com/dba/hostel022017.en.htm