Frequently, I have returned to hotels later the same day I checked out and asked for a key to use the gym and I've never had any issue with this at all.

On at least 2 occasions, I approached Marriott properties near the airport and very frankly told them that I wasn't staying at the hotel on this trip, but that I am a very loyal Platinum Premier, and asked if they would mind giving me a key to the exercise room. In both cases, they were happy to oblige. In one case I walked over (hotel connected to airport), and in the other case, I called ahead and then took their shuttle over (at their suggestion). I thought this was excellent customer service.

One thing I have noticed, however, at least at Marriotts is a decreasing number of properties with showers available in the exercise room/pool area. That makes this plan more difficult to execute.