I think I'd bring my own lock for my gym locker regardless, but if I decided to lock it in the car, either an unobtrusive locked case/safe somewhere in the passenger compartment or the trunk would be my choice. There are those black unmarked cases that cable lock around a solid frame piece (I forget what they're called or who makes them, but I've seen them at Sportsman's Warehouse) or Brinks makes a punch-button combination lockbox you could bolt in as well.
If I decided to carry the whole time, I think I'd find an area where I was pretty much in a corner and could only be viewed from one side, then keep my gun side toward the corner. Most folks seeing you changing (breaking the man laws or not) will assume you're a cop and pay no mind, but I am sure someone would bring their young son to the gym and you'll eventually get, "Hay Mister? Are you a policeman?"
Prime teaching opportunity, that. "Nope, but I'm still one of the good guys."
Blessings,
B