Sports (in some aspects) needs facilities, gear, arenas, other people to participate with. Building things usually requires materials (unless you're bushcrafting) that requires a fully-functioning supply chain. Video games and shows and films (at the quality level we expect them to be) require herculean efforts from thousands of people each, and massive investments, to go from concept to completion. Travel in and of itself is predicated on the ideas that the hospitality industry exists, infrastructure for flight, rail, bus, car all exist (and are operational), that the very people that are the fabric and heartbeat of the culture you're traveling to experience exist, and are operating restaurants, businesses, etc.
Every leisure activity that we think of occupying our time with instead of a job requires the collective efforts of the rest of society to even exist, and kind of implies that your ability to lead a life of leisure is an anomaly. Some things can arguably be replaced with AI and robots, but the texture and tactility that we crave from most of these activities would be gone. Traveling to Scotland to get a plate of haggis and hang out in a pub just wouldn't be the same if your driverless taxi took you to the unmanned airport full of kiosks and humanoid sentries, to be loaded half-conscious into a metal tube and flown across the planet, ultimately driven to the ends of the Earth and dropped off at a 600 year old crumbling building where you're met by R2-D2 wearing a kilt and a tam o'shanter, talking like Groundskeeper Willie LOL
I'm not sure I follow the logic here. I would still see all of this existing and even more due to demand. The idea with automation would be that everything that people want would still be there and even more. I would think we build more football stadiums, more hobby facilities, replacing business offices and other things we don't need with those.
I would also see e.g. video games being even greater than they are now, because people would be able to follow their passion and creativity and build games that won't require monetization and are unaffected by outside pressure. I have massive amount of video game ideas that I think would be super awesome, but not really easily monetizable. I would probably build a lot of them, especially with being able to do those so much faster with AI. If AI can do all the games by itself and doesn't require my or anyone's creativity, then super, I will just play them, because by definition they have to be better than anything so far, and if they are not, then by definition human creativity still matters there and they can build, either way seems good to me.
As for travel, I think there would be people out there doing this out of hobby, having pubs as a hobby thing, hosting people as a hobby, spreading their existing culture out of passion, not because they need to make money. I would actually prefer that type of travel over feeling like they only act friendly to me because I will be paying to them. In this case it would be visiting people who want you to visit them with no exchange of anything, both sides would be doing it out of curiosity or desire.
I can tell you, freely, that if someone dropped $10m in my lap, I would not stop programming - I started before I was paid, and I will continue as long as my input methods, perception, and/or brain permit.
The difference is in the quality, texture, and structure of how you work, and of course what you work on. I almost certainly would be working in the structure of larger organizations.
There is some interesting post-scarcity fiction out there, speculative and otherwise, that tries to answer the question "what do we do when we are no longer required to work for pay". Manfred Macx would say that it's great fun to make other people incalculably wealthy. Or, you could simply be kind and generous with your time in service to causes you like.
Frankly, if someone dropped $10m in my lap, I'd almost certainly take 2-3 months sitting on the beach, but after that, I'd try something even more ambitious. Surely there are hard problems we could be solving that we're constrained by paid work from pursuing.
I'd probably also expand my hobby practices - there's lots I could do with better tooling and toys (my pottery studio could use a pugmill!), and discover new ones as well.
For me personally, having the right job is actually more interesting to me than doing whatever i want all day then given my conditioning. I think because without the job I wouldn't have the same opportunity to encounter the "problems" i enjoy "solving" at work with critical thinking. It's kinda like training for a sport? Sometimes having a competition or a game is a nice forcing function to make it all feel real?