Grapes can safely sit out for around 2 hours although they can remain safe out at room temperature overnight.
But it's best to refrigerate the grapes if not eating or serving the grapes within a few hours.
Grapes should not really be left out longer than a few hours.
Although I have left out grapes overnight and they were safe and okay to eat the next day.
Grapes can safely sit out at room temperature for 2 hours so you should either eat the grapes within 2 hours of them sitting out or you should refrigerate them.
If you leave the grapes out longer than 2 hours at room temperature the grapes can start to go bad and grow bacteria on them.
Always keep the grapes refrigerated until ready to eat them and after you buy the grapes from the store you should get them refrigerated within 2 hours of getting home.
However I have left grapes out all day while eating them but if you're not gonna eat the grapes within that same day then to keep the fresh and prevent them from going bad you should refrigerate them within 2 hours.