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.
The Twentieth Street Recreation Center is about nine blocks away from Union Station at 1011 20th Street (20th and Curtis). It is classified as a "local" rec center; the fee varies by age, but it's no more than $5.50 at present. As far as I can tell, you are not required to be a resident of the city or county of Denver to use the centers, though only residents are eligible for certain programs and promotions. They will not have towels, however.
There are many health and fitness clubs in LoDo, the neighborhood closest to the station, and you can inquire with them about guest access, but any of the municipal recreation centers is likely to be cheaper. A little farther away is the Downtown Denver YMCA, which offers day passes for $15.