I wouldn't. Typically schools only have a few students willing to host, so the polite thing to do would be to leave it to someone traveling. Also as a student I would be a bit confused why you wanted to sleep on my couch the night before a bit interview when you lived 10 minutes away.
If you have questions about the school you can ask students during the interview. Feel it out, most schools have a few students who will give out e-mail addresses and stuff if you want to contact them for specific questions.