If you are willing to ride the monorail around to the Grand Floridian Villas, the new Spa is in a separate one story building right across from the Villas entrance. The fitness center is on the right side and is the nicest one I have seen so far at Disney. It is also immediately adjacent to the villas parking lot, the grilling area and the BB court.
I saw one person using it. When I walked in to take a look, staff were immediately attentive. They also gave me a spa tour.