Price of a cab to the Westin? 150RMB? Not really. Depends on which Westin. Should be half that to the Westin on ring road 3 north.

All discussion about fees is irrelevant. what counts is the net exchange rate that you get. In some cases you are better off paying fees for a good exchange rate.
The exchange rate of the banks at the Beijing airport is very close to what one would get in the city but it is much faster. Unlike most airports in the world, it is actually a good place to exchange.