I am aware that many Starwood properties (including most of the domestic Ws, I believe) allow for pets, but my understanding was that the room would be treated after the guest left, and that the fee was much more than the OP suggested. I personally am not thrilled at the prospect of noise from other pets in the hotel... but would be fine with staying in the room after if it had been treated.

I just found this from the W's web site:

Please be advised that the room rate with a pet is $25 above the room charge plus a non-refundable $100 cleaning fee.