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