DH and I used the gym at the Swan in Nov. It's small with just a few treadmills and weight machines, but it we were able to get in a decent workout because it wasn't crowded. It's located in one of the last rooms in the Swan on the way out to the Grotto Pool.
The Swan has a small work out room on the bottom floor, near the pool, as Bedknob suggested, but guests can also use the big health club at the Dolphin, which has whirl pool and massage rooms and work out machines.