I haven’t been a member of a gym in a while, but I have a great little bag that was a hotel bonus from the Art Hotel in Amsterdam, which I used when I was going to a pool for swim sessions. Not very helpful to you, though.
Tagging on… I’ve been on the lookout for something similar, a replacement for an old weekend bag that just bit the dust on my recent road trip — the zipper finally gave up and broke right off. I’d had it for at least 12 years, maybe more like 15. It was by Dav and used to also have a matching umbrella. They made rainboots too. Not even sure if they are still in business, but I would repeat that purchase in a heartbeat. It had great zipper pockets on the outside, easy to clean, and a bright inside so it was always easy to find things in it (why are so many bags lined with black or dark colors?). I liked that it had a removable flat panel in the bottom to help keep its structure when it was empty, and that it was a duffel shape with wide access. I don’t like anything that has too narrow an opening, so you have to pull out other things to get to what you need.
One thing that bag didn’t have that I would like next time is a zipper that zips from both sides — makes it easier to open and close when it’s very full.
So as I’m keeping an eye out for a good weekender bag, I’ll keep your gym bag requirements in mind too.