There is more to D&D then killing things for XP. The D&D story doesn’t always have to be about swinging across a chasm while kicking a yeti in the face. The classic adventure tale is amazing and is the core of the game, but we are not limited to it. We can use the framework that the game provides to tell all kinds of different stories.
Drama
The classic conflict of words and intent. It is incredibly easy to build drama infused stories simply by having NPCs that don’t like the adventurers whom the adventurers can’t kill. It is so much fun to see players react to NPCs taking socially acceptable and technically legal steps to make the player’s lives miserable. Will the players do something below board to have vengeance on them? If so what happens when they go to the authorities? And this is all just from antagonistic NPCs!
What happens when a friendly NPC reaches out to the characters asking for help in covering up a crime? How do your players entertain themselves at the royal ball that they are required to be at? When the military shows up to draft someone from your family, what do you do when your 13 yo brother offers to go off to war so that you can keep adventuring? How do the adventurers then handle their parent’s resentment for sending their youngest child to their death?
Comedy
D&D bleeds comedy. Every awkward roll and quirky magic item can be adjusted to add levity to the story. Here are a few things to keep in mind if you want to add a bit more humor to the game.
The easiest method is present them with an incredibly petty quest. Have a bartender offhandedly say, ‘those priests are SOOO prim and pious, they don’t have a speck of dirt on them. Wait a minute, your adventurers right? I have a cart of manure out back and a job for interested parties, if you’re picking’ up what I’m puttin’ down.’ Giving the players a chance to troll various NPCs is great, and I have yet to have a group let the opportunity pass.
Just have NPCs around who are arrogant, judgement, materialistic, self-centered, dismissive, and/or entitled. The players will take up any opportunity to ruin their day since straight up killing them is gauche.