Well, I’ve never been in the military, so I don’t know what ‘real’ WMR is, but here’s what we have so far:
In the TOS episode ‘Shore Leave’ the crew finds a planet that is designed to be a ‘shore leave’ planet. Anything you want is created for you. Just don’t let your mind . . . wander. Also, in the TAS episode ‘the practical Joker’ we find out that the Enterprise has a sort of ‘proto-holodeck’ that can make different environments for you to walk around in, like a nice forest or sunny beach, or cold mountain. Course, the canonical-ness of TAS is . . . questionable.
In TNG and DS9 (and ENT come to think of it) We hear of (or see) Risa, a pleasure planet, where it is . . . heavily implied that casual, consensual sex is not only available there, but encouraged. It’s also got beautiful views and great beaches, sunny skies . . . etc. Many officers take their shore leave there.
Earth is said to be almost a paradise with no wars, no poverty, and good food, and many take their shore leave there (including Sisko.)
As for sports, Captain Archer enjoys Water Polo and hiking/ . . . psuedo climbing. He likes . . . I guess scaling small mountains is the right word. It’s not free climbing like Kirk, but it is physical activity. T’Pol practiced a form of Vulcan Martail Arts (I forget the name.) We see the crew of the ENT playing Basketball at one point in a Cargo Bay, with Phlox being the star player due to his superior hand-eye-coordination. Also the MAKOs introduce a target practice game in season three that several people like.
Michael Burnham is shown to jog laps around discovery to get a Runner’s High (taking Tilly with her sometimes) and to keep in shape.
Sulu and Pickard do fencing, Kirk does free climbing if Star Trek V is to be believed.
Worf teaches Mok’Bara (essentially Klingon Tai-Chi) to Dianna Troy and Dr. Crusher. Like I said O’Brian does kayaking, Worf and Guinan do target practice with phasers, and as someone pointed out, Riker plays some sport called ‘Paricies Squares’ which . . . I don’t think we ever see on screen.
Like I said earlier Sisko and his son enjoy Baseball (along with Cassidy’s brother, there are, I think she says six baseball teams on the colony he’s on?) And then Kira, O’Brian, and Bashir all participate in a Bajoran sport called ‘springball’ which is . . . basically Tennis except you knock the ball against a wall and rebound it to your opponent’s area instead of over a net.
We don’t see much sports on Voyager . . . which is no big surprise because they are trying to get home and don’t have much time for shore leave. They mainly use the Holodeck, but at some point Tuvok mentions that he does Archery and even taught it as an elective in Starfleet academy for a while.
That’s all I can think of.