I'm in Austin several times a year. I used to stay at Oak Forest http://www.robertsresorts.com/resorts/oak-forest-rvpark/ but haven't been there in over a year. It was "just OK" then but ownership has since changed and I'm reading that good changes are afoot. It's still located in a part of town that's a shopping desert, though.
My favorite park is La Hacienda http://www.lahaciendarvpark.com/ which is a 30 minute drive to downtown on a good day, but is a beautiful park with decent shopping reasonably close by.
Stayed at Lone Start some years back. Decent park, but traffic into and out of downtown makes it no quicker a commute than the more outlying parks.
Getting a spot anywhere near Austin on short notice is tough at best, and impossible when there's an event in town. Austin has lots of events through the year.