There are actually tons of courts on the Stanford campus itself. Some of these are often accessible by the general public. Taube Tennis Center
, with 11 courts is on Campus Drive (East) near Galvez. Across the street is Taube South
with another 6 courts. There are another 8 courts at the Stanford West campus courts
facility. These are just off West Campus Drive (on Electioneer Road near Junipero Serra Blvd). There are other courts on the campus as well but I'm not sure if they are accessible to the general public.