On this page of The Witcher Monster Slayer guide, you will find information about the time of day and how it affects quests and monsters.
Time of day
More dangerous and rare monsters come out at night. At night you will encounter more legendary and rare creatures with high difficulty levels.
It's worth saving stronger oils, potions, and bombs throughout the day to use on nocturnal monsters that will fight you with all they have.
Dawn and twilight
Time of day doesn't just affect monsters, however. Some quests have specific requirements, such as you must show up at a certain location when the sun rises. You can't ignore that.
To determine what time it is dawn/dusk, you can look it up by typing a given term into Google, such as "dusk [date] [location of interest]". Use this knowledge to plan when you want to complete the task. However, consider a 20/30 minute time window, preferably before and after that time.
On rainy days, you can encounter more monsters on the streets. Some types are more likely to appear when it's raining.
Remember that going out with your phone on a rainy day, let alone in a storm, is a bad idea.