Childcare during a show?

I am a single father of four. My kids are obsessed with Wicked, so I am planning an overnight trip so I can take them to see the show on Broadway. The problem is, my youngest is three. I don't know if this is a thing, but are there any safe/reputable child care services that could take care of her while I have the other three at the show? Because we're just going for an overnight, we won't have a hotel room at the time of the show. Thank you!