Where are you coming from?
Are you asking for the cheapest flight?
Are you asking for cheapest way from the Airport?
Look in to TF Green airport in Providence and Manchester, NH airport. Southwest flies in to both and could have decent fares from wherever you are.
Logan airport in Boston is the closest airport to BU. A cab ride to the BUMC area runs about 20-25 with tip and fees. There is a subway that could get you close for only a buck, but it takes time and patience.
I don't know anything about student hosts.