The hospital I work at does offer is the day after birth. They do it the following morning. You have to be NPO (nothing to eat or drink) after midnight, and you will have IV fluids going, then they take you for the procedure 1st thing in the morning. Typically it doesn't make the hospital stay any longer or anything.
A lot of people change their mind when they find out they will be awake from the procedure. They will not put you under that close to giving birth. If you wait until your 6 week post delivery visit, they will. Not sure if that matters to you, but a lot of moms choose to wait when they find that out. GL!