Mini side-quests

A few random ideas:

Getting food in the local tavern. This can be really fun especially if you pull together a menu and play through describing the food. Throw in a silly magical food for fun effect (a pie that changes flavor every time you take a bite, an ale that makes the drinker levitate slightly, etc).

Helping the local wizard or alchemist find a necessary material component. The component can even be pretty easy to find (in the woods outside of town or in another shop in town), but the wizard is agoraphobic and so sends adventurers out instead. That way, the hunt can be minimal and the roleplaying and negotiating with the wizard can take up the bulk of the 10-15 minutes.

Attending a shindig of some sort: a royal ball, the grand opening of a new building in town. These can be great because there should be local bigwigs attending who the PCs can do a lot of social roleplaying with, but it can also be used as a scouting mission (to gather intel on a person who is attending, or scope out the place for a heist later).

If the PCs are already "on the road" then the 1 or 2 PCs that are taking one of the night watches can have a small adventure. Maybe spooky sounds in the woods lead to a run in with non-threatening forest-dwelling humanoids. Elves, gnomes or halflings out gathering some night-blooming plants could end up being conversation-heavy interaction (as long as your party isn't too quick to roll for initiative).

Let me know if any of these are what you had in mind.

Hunting for dinner/hides is always enjoyed by my guys. If you want to add a little more, once they kill the deer or rabbit or whatever a predator, lion or a pack of wolves, whatever, can show up to take the kill for themselves.

Also, this is a good time to draw from those randomly generated side quests from those open world RPGs, such as the Witcher, Skyrim, etc. I think Skyrim does it particularly well since they have these little quests made for each of the factions, be it the magi, the companions, assassins or thieves. You could always draw on the PC's backgrounds to make similar quests, rather than using their classes to do so. For example:

Acolyte: A shrine located in the outskirts of town (or on a stretch of road between towns) has fallen to disrepair. The local priest asks you to kindly restore the shrine to your god, as doing so would grant you a small blessing that lasts 24 hours.

Charlatan: A former victim of you devious schemes unfortunately figured out who you are, and threatens to expose you. Deal with it.

Criminal: It is time to pay your dues to the thieves guild. Alternatively, the guild informs you of a potential lucrative heist in your area. Or, knock knock, the guards are at your door.

Entertainer: The tavern owner offers you some extra coin should you entertain his guests. Or, a musical/storytelling festival is happening in town, and your expertise are required.

Folk Hero: Low leveled monsters are terrorizing the fine folks of _____, deal with it, hero.

Guild Artisan: When was the last time you actually MADE something? Well, here's a chance for you to make a name for yourself.

Hermit: Despite your best efforts to uncover some universal truth, it evades you still. Rumors have it that the entrance to a complex of ancient ruins exist close by.

Noble: You receive a letter from your parents asking you to court the heir of a powerful noble house. Good luck.

Outlander: An interested scholar wishes to learn more about your culture. Spend your day entertaining him and get free lodging.

Sage: You have always engaged in a friendly competition with this particular student during your studies. Why let a little adventuring get in your way?

Sailor: Your landlubber companions had garnered the ire of the local fishermen by breaking superstitious believes. It is up to you to make peace.

Soldier: Are you a deserter? If so, then a couple soldiers are looking for you. If not, then a couple of deserters show up in town. Do with them what you will.

Urchin: You see an older teenager forcing younger boys to pickpocket for him at knife-point. What do you do?

These are just some that I came up with off the top of my head. I have found this particular product on the dmsguild quite useful for these side-quests/random events sort of things. Go check it out and see if you like it!
Character Focused Random Events for the City