Well, i don't know if it's the most expensive city, there're also New York and Honolulu. But I know it's one of the most beautiful in the world.
The latest influx of the new riches (Silicon Valley) have driven up the price of the real estate in the "City" and the South Bay (Palo Alto, Santa Clara, San Jose etc.) but Oakland is in the East Bay so it's still fairly reasonable (but then again, I've lived there (SF) all my life (not presently, however) so I don't really see the differences as compare to one that has just arrived from the Midwest.
You can probably find reasonable housing in Alemeda area. That's where most of the students stayed during my training there.
You don't want to live in the "City", that's what folks in the Bay Area refer to San Francisco. It is too expensive and the commute is impractical (gas, toll, time).
I hope this bit of info helps. Good luck.