This is obvious: Better food is found off campus! For listings and reviews of places to eat off-campus, check out the can't-be-beat Guide to the Good Life at Stanford, and the local newspapers (e.g. Palo Alto/Menlo Park/San Francisco Weekly, The San Jose Mercury News, The San Francisco Examiner). You will certainly discover your own favorite places, but here are a few finds. Eating out is not cheap around here; the recommendations below are not based on cheapness per se.
The Peninsula Fountain and Creamery on Emerson Street P(alo) A(lto) is an all-American burger and milk shake joint. A more low-key burger joint is Jim's Coffee House, on University Ave. Both places serve breakfast all day.
Nearby, Jing Jing's on Emerson Street PA is a good bet. Szechuan Palace (Lytton Ave, PA) seems to be a departmental favorite. Castro Street in Mountain View has a whole string of Chinese restaurants. Try The Noodle House (the food is actually cheap).
For dim sum, Ming's on Embarcardero Road PA is the best locally, but it's very expensive.
Again, Castro Street is the place to go for Indian food. Sue's Indian Cuisine is pretty good. One block before Castro Street on the left on El Camino is Passage to India, which has a really cheap lunch buffet (around $5).
Il Fornaio Cucina Italiana (Cowper Street PA) is ritzy and has pasta and grilled foods. Carpaccio on Crane Street in Menlo Park has better food at higher prices.
Sushi Ya on University Ave PA has a good reputation for sushi. Down El Camino in Menlo Park, the Gombei Japanese Kitchen has very good cooked dishes (mostly rice and noodle dishes) at a reasonable price -- no sushi here.
Ándale right on University Ave PA has a variety of burritos and dinner combos --- they're much better than those served on campus at the various cafeterias, and the price is good.
Applewood Pizza (El Camino Real, Menlo Park) has a wide variety of pizza toppings (and beer). Ramona's (Ramona St, PA) is a Palo Alto favorite. There's also Ramona's Too (Birch St, PA), which offers take-out and delivery.
Bangkok cuisine (407 Lytton, PA). The one in Menlo Park is nice, too.
We don't know of any strictly vegetarian restaurants nearby, but this being Northern California country, most restaurants provide vegetarian selections.
The Rose and Crown: that's the mock-Tudor building in the parking lot just off University Ave on Emerson Street.
The Empire Grill and Tap Room: a wide selection of beer at the full service bar. This place has quite good food too. The crowd flocks to this place, especially on Friday nights.
The ubiquitous chains are out there. Try the smaller cafés like Café Borrone (next door to Kepler's Books, El Camino Menlo Park), The Prolific Oven (Waverley St PA).