The CalTrain station in San Jose is within a reasonable walking distance of the Fairmont Hotel (or a very short cab ride). Perhaps your travel agent can find out more for you.
The following services were mentioned:
It turns out that United Airlines operates a bus from their terminal at San Francisco Airport to San Jose Airport, and also downtown San Jose -- and back: it's hourly, I think. It cost me about $10 I think; the driver said something about it being an even better deal if one is flying with UA.