I have just had some correspondence with Hostal Mirentxu on Zorilla-nearly same location as Principado. You might try that. Carlos Dominguez was the respondent, very prompt and cordial response to my e-mail inquiries.
Interesting name,Carlos Dominguez,anyone into the Austin acoustic scene knows that Tish Hinojosa has a song about him.
If you end up staying there, wouldn't mind some feedback, as I am looking to do so as well soon.