The fitness centers at the Westin Villas are more than adequate, although I agree with the advice to go for a run. I, however, would run north on Lower Honoapiilani Road rather than to the Hyatt - it will be much less busy and you can run for at least 5 miles (one-way) without hitting highway.
Also, as a practical matter, nothing prevents folks from the Westin Villas from swimming in the Sheraton or Westin Resort pools. I know from experience.