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.