In this game, if you move to the starting location at the correct time of day of a story that begins automatically, such as the main story or certain events, the corresponding story event will start on its own, and there is no way to manually prevent it from commencing.
Hence, if you'd like to do activities that overlap with a story's starting conditions, such as City Life activities in your room, please progress through the story first before engaging in said activities.
If you don't want to progress through the story for the time being, please stick with activities that do not overlap with a story's starting point (namely those that take place at a different time and location).
If you ended up skipping a story event, you can always re-watch scenes you've already unlocked by going to [Collections] → [Story Log].