If you’re a female, I would suggest the Hot House Spa on Capital Hill. It’s a small establishment but they have a steam room, sauna and jacuzzi. Plus, it’s reasonably priced and very tranquil. I usually go during the weekday afternoons when I can because there are fewer people. Sometimes I’ve had the place to myself. It’s one of my favorite places to relax in Seattle.
I second the recommendation for Hot House for women. It’s a small but nice, tranquil, clean space.
My one piece of advice is to either go alone or, if you go with friends, you should be versed in sign language! I’ve been scolded there for talking with my companions. I guess that keeps it tranquil…