This is a fantastic resource which I only found out about this morning. When we evacuated for Hurricane Rita, we were competing for hotel rooms with the population of the Houston and Galveston area which were also evacuating. All hotel rooms were booked all the way to Dallas.
Click here to see hotel room availability in Texas during emergency situations. I can't vouch for the accuracy, of course, but I'm going to assume it's a good indication of room availability.
Update on our evacuation plans: My mom, dad and sisters and I are staying put. My aunt and cousins in Port Arthur are going to Dallas. I don't know, yet, what my cousins in mid-county are doing. My guess is they won't be evacuating either.