Exchange students should register with the student accommodation centre, WoVe, the accommodation service of the University of Basel. For a small fee, this organisation will assist in the finding of a separate furnished room or studio, or a room within a communal flat.  The rental for such accommodation is between CHF 300-600 per month.  WoVe also maintains information exchange platforms.

Other links for students looking for accommodation are:
www.students.ch/wohnungen
www.wgzimmer.ch
www.immobilien.bs.ch 
www.unibas.ch/wohnen
www.clickLodge.com