Ways to obtain off-campus housing include (i) friends; (ii) the off-campus housing office (whose files are also available on-line in Folio --- you don't need to go in person); (iii) newspapers, (iv) bulletin boards such as those at Tresidder and Printer's Inc.\ (see Bookstores), and (v) driving around local neighborhoods looking for For Rent signs. If it works out, (i) is the best; for renting a whole place, there are generally better deals to be found in (iii) than (ii). The strongpoint of (ii) is when you want a room in an apartment or group house. Be wary of ``contract-listing'' firms that give you listings for a fee---generally a waste of money.
There are various neighborhoods with rental housing. Closest to Stanford are College Terrace (across Stanford Ave from Escondido village) and nearby sections of Menlo Park. Either of these, and anywhere in downtown Palo Alto, is expensive. Cheaper rents can be found by heading any direction except west---to Redwood City, East Palo Alto, or the eastern fringes of Menlo Park that are unofficially part of East Palo Alto, or south to areas like Barron Park and Mountain View. East Palo Alto is the least safe, but probably cheapest place to live around these parts. Many students actually live there, and the area is being developed. Many people find it safer to drive at night there, rather than walk on the streets. Be alert when biking.