There are a Sheraton and a Westin right next to each other that are the closest hotels to Stanford (if you don't count getting a room in the faculty club!).
Still mostly too far to walk to campus, but there is a regular free shuttle run by Stanford during the day from the Caltrain station a block away. Both are also walking distance from downtown Palo Alto. Make sure you don't get a room facing the RR tracks, unless you like being awakened by trains starting at 5am.
The nearest Marriott is a brand new Residence Inn about 3 miles South on El Camino, and there is also a Courtyard that is either open or almost done.
Nearest Hilton is a Garden Inn about 5 miles south of the Residence Inn in Mountain View.
All of these hotels are on El Camino Real (that's the name of the street).