Despite the cold weather and urban grunginess, you'll be pleasantly surprised at what you find. Locals may put their nose in the air, but you'll be so enraptured by the city's charms, you might not notice. The Bay Area, which SF is commonly referred to as, actually consists of a large stretch of land surrounding the San Francisco Bay. At the heart is the peninsula of San Francisco. The Golden Gate Bridge connects San Francisco to the northern communities of Marin County and Napa Valley.
East Bay refers to Berkeley, Oakland and beyond.
South Bay, where the international airport is located, consists of Daly City south to Palo Alto. Below Palo Alto is Silicon Valley, a sizable portion of which is San Jose. I like it a lot. I like it. It's not very good.