Downtown Palo Alto offers some wonderful restaurants, cool boutiques, pharmacies, the Aquarius and Stanford theatres, and a Saturday farmer's market.
California Avenue features two natural and gourmet grocery stores, small cafes and bookstores, and a Kinko's for that late night photocopying.
Town and Country Plaza on El Camino and is an ivy-covered maze of restaurants, small shops, and offices. Watch out for those Paly students loitering around JambaJuice!
Mid-town Plaza on Middlefield boasts groceries, bakeries, Papa Murphy's pizza, and a small video rental shop with prices more reasonable than Blockbuster.
Menlo Park's downtown area offers a Sunday farmer's market and Trader Joe's, two art film theaters, and several wonderful bookstores.
San Antonio Shopping Center in Mountain View is a less upscale shopping environment--Target, Sears, etc.--where you can pick up a lot of basics for your apartment at a reasonable price. You'll also find a Safeway, Rite Aid, and Tower Records nearby.
Castro Street, a little further east of San Antonio Shopping Center, has some excellent and inexpensive places to dine and to shop for ethnic specialties.