No vacancy? Not always. If the hotel you really want to stay at is completely booked, try discretely asking whether or not they have any “out of service rooms” they could rent to you.
“Out of service” is the industry term for a room that, while vacant, has been set aside for repair. Hotels won’t offer this up front, so you’ll have to inquire politely.
Obviously you’ll want to determine exactly what the problem is — but minor things like a carpet tear or stain can be overlooked easily for a reduced fee and a comfortable night in the hotel of your choosing … particularly if the location is prime.