Showers near Denver Union Station?

We are planning a trip for later this summer via Amtrak and are planning on stopping in Denver. But we're traveling in coach, so will not have access to the on-board showers on the train. Do people have suggestions on if there are showers near to Denver Union Station that offer privacy and towels for a reasonable cost? I'd though about looking to see if there was a health or athletic club we could contact and pay a few dollars to use their showers, but not sure if there might be other options within an easy walking distance.