Incoming Stanford postdocs looking for long-term lease starting July 1st @stanford.edu

Hello! We are two incoming Stanford postdocs seeking a long-term lease starting July 1st with the following preferences (although very flexible):

-2 bedroom or larger 1 bedroom unit
-in unit washer and dryer
-private outdoor space (patio/yard/etc.)
-unfurnished
-monthly rent <$3600
-located near to campus (Palo Alto / Menlo Park / Redwood City / Mountain View)

We have a cat and a dog (friendly, calm, and pleasant 8 year-old Border Collie mix). Both pets are very polite; we can provide a reference from our current landlord.