I am, of course, thrilled that BART has finally reached SFO. Though it pains me to say it, I cannot recommend BART as a solution to the OP's question.
BART will not get you very close to Nob Hill and while you might be able to flag a cab at one of the city BART stations, this would not be a very convenient or pleasant introduction to the city. I would second lihue1k's suggestion that a cab to your hotel from SFO is the way to go.
As for touring outside the city (Marin?, Napa?, Palo Alto?) I would imagine that renting a car would be both less expensive and more flexible than a limo unless you are on a truly unlimited budget.
I hope you enjoy your stay.