Thanks! Mannheim is close to the first place I ever went in Germany (which was Schifferstadt, like, just a few kilometers away). I may have actually been there, but it was in the middle of this 3-week school trip, so we saw a lot of things. And it's cheap to get to from Frankfurt, yay.

http://www.bedandbreakfast-mannheim.de/bb/preise/ looks rather günstig! Doesn't include breakfast, but it says they have a kitchen guests can use. It's only a few tram stops away from the GI or a ~1 km walk (which might be unpleasant in February). (I'm not very good at doing what I'm supposed to be doing. I keep getting distracted.)