Also Foothill College housing may have some leads:
A short term rental may be especially difficult to find near Stanford. Further away there are a number of businesses catering to business clients who stay for a few months. I don't remember the names for certain but I believe extendedstayamerica.com or suiteamerica.com could get you something.
Palo Alto real estate and homeowner information at: http://julianalee.com/palo-alto.htm
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To go directly to the Stanford University off-campus housing page you can click on the following link: https://places4students.com/Places/School.aspx?SchoolID=hlga
For more information on off-campus housing near Stanford travel here: http://www.stanford.edu/dept/rde/cgi-bin/drupal/housing/?q=c