hi potato
have you looked into the university library? if your residence is registered here, you can get a card there for about 7 euros and you would have not only borrowing priveledges, but also 24 hour access! Even without a card, you can go there to study during regular business hours, student or not.
http://www.ubka.uni-karlsruhe.de/index_engl.htmlThe Landesbibliothek is also quiet, but it's not my favorite place to work because you have to lock up your bag to enter the library, and I find it to be a hassle.
http://www.blb-karlsruhe.de/good luck,
ann