Call the hospital you'll be heading to and ask to speak with a nurse about it. I think a lot of these type of places are run locally, rather than nationally. (I don't know of anything national, other than Ronald McDonald House, but I think that's just for kids, right?) My hospital has something like that called Amanda's House.
http://www.glensfallshospital.org/Commu ... _House.htm
A lot of hospitals also set up deals with local hotels for patients.