Here's how I got my room at the Courtyard Marriot, walking distance from the Mission Palms:
After I called and they said they were booked solid, I went to
www.hotels.com and searched for the nearest hotel to the Mission Palms. Just type in address "60 E 5th St., Tempe AZ".
Turns out that through Hotels.com, the Courtyard still has rooms available. Check it out. They must have an agreement where hotels.com gets a certain amount of rooms no matter what.