For the homes, I would say Pacific Heights, Presidio Heights and Russian Hill. For the shopping areas, I would agree with both of the other answers.
You can go to http://www.sallyrosenman.com for a full description of all the areas of San Francisco.
In my opinion, San Francisco's Russian Hill begins to have similarities. Hyde Street and Polk Street have the very beckoning restaurant scene, very neighborhoody, very walkable, the requisite coffee shops, and architecture that spans Victorian, Edwardian and mid-century walk-ups. The architecture also encompasses several high-rise, full-service, doorman buildings housing some of the City's society-folk.
Nothing compares to New York's Upper East Side, but San Francisco's Russian Hill is a good start. Happy Hunting! Paul
Having lived in NYC for a couple of years I would have to say that Pacific Heights is the most equivalent to the Upper East Side both in demographics and culture. However, you could also make a case for the Marina, Russian Hill, and even Nob Hill to some extent. Please feel free to email me at firstname.lastname@example.org if you need more in depth descriptions of the different neighborhoods in San Francisco.