The mechanics of Dungeons & Dragons don’t force you to choose a pastime or hobby. Outside of Bards and the various Backgrounds that include entertainment and arts there is no obligation or hint that a character should do things besides fight, interact socially to solve or cause problems, or explore a wildernesses and dungeons.
With a limited number of skills and tools you might weaken your character if you take something without a direct impact on their ability to perform as an asset in the adventuring party – so what?
Be a tiny bit weaker and add something that your character enjoys doing that has nothing to do with defeating dragons or wandering dungeons. In the real world in the eras upon which D&D reflects, this was common. Commoners worked less than we do in the modern era.
There’s a reason that there are giant stadiums more than a 1,000 years old scattered around the world.
But it’s more than just sports.
They sang songs. Told tales. Wrote dumb epic poems that we still read.
So what does your character do when they aren’t living their life and when they aren’t dungeoning or dragoning?
Burn a tool or skill on this – or don’t! – maybe they enjoy doing something that they are bad at.
Maybe your next PC or NPC is the world’s best tafl player, or the local community’s worst singer. Maybe they make little sweaters for the elves that aren’t actually elves, and then they meet real elves. Maybe they are the old man that talks story to the children of his town.
These elements may show in just a sentence or two in a given gaming session. That’s okay. It’s part of who they are and what they do, even if a d20 isn’t involved.