If your child is wide awake the whole night, what activities do you do with them?

Hey, I guess, keep singing lullabies one after the other in the hope that at some point of time he will sleep. ;p Else, you can just the baby be in her nursery. Let her play with her toys till the time she gets exhausted and go to sleep. Till that time you can lie down on a bean bag nearby or put a mattress on the floor so that even if you fall asleep, you know that baby is on the floor and would not fall off the bed.