When on a tour abroad, we often take the hotel for accommodation. The usual check out in the hotel is 11 am and if our flight is at night then we still have extra time. What we do is to check out on time and then leave our things with the hotel concierge so we can spend the remaining time in roaming around. But beware because there are hotels that charge for the safekeeping of baggages. In Hongkong, that’s what we did when we checked out of Guangdong Hotel. We were being charged 5 HK dollars for each bag that we would leave there. Come to think of it, we were hotel guests who had just checked out huh. That’s unfair.
I have booked out at eleven and stayed until three and it was okay. Staying for an extended period after book out time may be a problem because you may be adding unwarranted congestion. You have to be cognizant that you had entered into a contract to leave at a certain time, therefore, the hotel would reserve the right to insist that you leave or impose a penalty if you were allowed to stay beyond the expired time if they would wish to. It's just business.
I have faced this situation in my long traveling career buy fortunately I never paid for cloakroom facility provided by hotels. However if I had to travel by train and I was to pass my time near rail station I always took the advantage of keeping my luggage in Railway station's cloakrooms. They charge a small amount but save lot of time as well money that way.