I tried finding this a few years ago when my travelling was at is peak. I did not find anything that would work for me. It always seemed like the affiliated clubs were really inconvenient for where I was working/staying, if there were any at all.

Many of better hotels have an affiliation with a nearby health club/gym. Basically the concierge or front desk would arrange for a day pass or week pass (usually at some cost). That worked for me in some places. Maybe that would work for you.