On having a car: I respectfully disagree. Texas is not very walking friendly, especially if you are used to an area that is (I am from Chicago and like to walk everywhere!). I like to explore the area around (lots of State parks, craft breweries, etc) which would be very difficult without a car. Additionally, walking even a block (a Texas block, which can often be 1/2 mile) can be unbearable in the summer. Parking is actually relatively cheap - about $10 a month for a student permit! The downside is that you are limited in where you can park, but definitely more convenient than where I went to undergrad (>$400 per year and you were only allowed to park in 1 assigned lot!).
In addition to Zipcar, many students use Car to Go (<https://www.car2go.com/en/austin/>), where you pay by the minute for a smartcar. There are a ton of these all over town; the downsides are that they are not well maintained (especially due to students driving like maniacs to minimize their minutes) and while you might be able to find one to get somewhere, you most likely will not find one when you are trying to go back home.
Austin is a really fun place to be a grad student! Great specials everywhere and lots of inexpensive activities to do in your limited spare time. However, it took me a while to get used to the heat in the summer and having to drive everywhere.