The Collaborative International Dictionary of English v.0.48:
Hospitableness \Hos"pi*ta*ble*ness\, n. The quality of being hospitable; hospitality. --Barrow. [1913 Webster]WordNet (r) 3.0 (2006):
hospitableness n 1: having a disposition that welcomes guests and is fond of entertaining [ant: inhospitableness]