Whether you could stay in a hall depends on whether your visit is planned for term-time or a vacation. Most colleges have a "guest room" or two which is not assigned to a student, but these are usually booked way in advance for visiting lecturers, etc. In a vacation, there are more student rooms free which can be booked by visitors.
Be warned that some rooms will be breathtakingly nasty, others lovely, and all will be quirky in some way.
Cambridge has a conference page (
http://www.conferencecambridge.com/home/); you can see where the colleges are and what kind of rooms they have. On your own you won't get the conference rate, but there should be contact details for enquiries.
If you're working with someone, or have a university contact (i.e., archivist) it's worth asking if s/he has a college appointment and could book a guest room for you.