Also consider that motel/hotel space is for the most part naught for the Austin area, at least those ones that list on the internet. Sister and I spent hours on the net and phone yesterday looking for space as far north as Temple with no real luck. I finally called one of my daughters in Waco and asked her to get out her local phone book and she found us 4 rooms at a decent local motel and we immediately jumped on them. On the internet there showed to be no rooms left after about 2PM for 200+ miles north of Houston. So, people might want to keep that in mind as there are still rooms available that don't list on the net.
Plus there is some sort of music festival scheduled for this weekend in Austin. Alot of rooms in Austin have been reserved for folks going to that. I would head north toward DFW where there are bound to be lots of rooms. I am inclined to advise my mom to stay in Austin. If she is going to leave, I would think she should do it this afternoon or evening.
That's true about the hotel rooms. I have a friend who is a travel agent and I was helping her answer phones yesterday. There wasn't anything available until somewhere north of Dallas which is probably Oklahoma now, or west being New Mexico.