Our Pauper always quizzes the front desk on when the property is most (and least) busy. You can do this on the phone, or drop an e-mail to the hotel you're researching via their customer service adress. But do it! Book in advance and avoid peak occupancy periods like the plague. Conversely, demand a cheaper room or a better deal when the hotel is in its slump period.
Remember, hotel rooms are perishable items. The management want rooms filled up; vacant they are simply useless inventory.
Avoid holidays, weekends, special annual events and summer. (OK---so summer may be asking too much, but if you can, travel South in summer, North in winter.)
Also look out for conventions and special meetings that can tie up a city, too. The local tourist bureau can inform you of what's happening in town. Room space is always at a premium when these huge conventions are underway. A savvy Pauper simply picks another location to visit when they can.