Most sizable hotels are going to have someone at the desk 24-7. Why book for the day after unless you want to check out after 12:00 noon in which case, you might still be able to do a 1.5 day for late checkout ? Basically, you should only have to pay for one night. There can be special circumstances if every room in town is booked for a sporting event, and then you might have to book way in advance.
This doesn't apply at all to daily rental apartments.
