I stayed at the he Tiny House on a recent trip home for the holidays (so have local knowledge of Austin and housing options). Lu's place is great - well located just off of Airport Blvd - makes it easy to get to and around town without too much traffic and noise, and the lockbox set-up is helpful because you can check yourself in and out without any hassle.
The space itself is spotless and stylishly decorated. Lu left some lovely touches in the kitchenette (snacks, coffee and the Chronicle[!]) and bathroom (robes and outdoor slippers) - which are both attached to the main property, but easy to go between and punctuated with a lovely patio to enjoy the winter sun!
Lu was really helpful and responsive to any query (including an offer of allergy medication!), but also respectful of privacy. She has a very sweet dog who will play if you're up for it (I was!), but was super well behaved too; I never heard it except when it was outside, goofing around with me!
This is a solid choice when staying in Austin.