I flew into the old airport last year and it was pretty cheap to just get a meter taxi from the queue.

I haven't been to the new airport, but the old one had a little quirk about taxis. There were two queue--one for very short range trips and one for all other trips. The Westin was an all other.

I stayed at the St. Regis and the Westin on the same trip (it started on the Westin's opening day). The Westin cost more than the St. Regis at that time, and the St. Regis was a far better hotel on just about every level.