My only suggestion is either book something before you get there or look for a hotel room early in the day.
We've decided to go at the end of August next year and are now trying to pick between two properties. I'm a bit obsessive so the hotel will be booked within the next couple of weeks as they have a very liberal cancellation policy (48 hours prior with no penalty).
I am extremely impressed with the number, quality and suitability of the hotels there. With an adult son we need a 2-br property which is usually difficult and expensive. I have found two hotels that not only suit our needs but get great reviews on TripAdvisor and won't break the bank.