After reading the previous posts and being a grandmother myself, I will be devious. This is YOUR time to be with your grandchild. We've gone with both grandkids but their parents were with us (damn it!) but we did have "alone" times with the grandkids. We didn't spoil them and we used their parents' rules but, well, maybe a few extra "goodies" came back with them.
One thing - make sure the child follows the same rules his parents have in their house. Yes, it's vacation and you want to spoil but - if the parents say "8:00 is his bedtime", then have him back by 8:00. If he shouldn't eat A, B, and C, then don't have him eat that because it looks nice. You've already spent time with him but he's changed since the last time you saw him so, get up to date with things. At three years old, he'll change with you before you give him back to his parents.
Take a camera and share photos with his parents. Text often. Have him talk to his parents every day, at least at bedtime because, at that age, that's a special time, and maybe in the morning to tell them what he's going to do that day. Have him share his enthusiasm with his parents because even if they aren't there in person, they are there in all of your hearts.