Looking for a private room + bathroom near Stanford (short term lease)

Looking for a private room + bathroom near Stanford University (within 10-20 min driving distance) under $1600 for a November move in. The lease should be a flexible month-to-month lease.
I am currently doing my Phd at Stanford and planning to move into a new place for 3-4 months.
Feel free to message me if you have an open room and more questions. Thanks!