1) Morris Williams "Mo Willy" - 4300 Manor Rd
A recently redone Austin Municipal (Muni) course. It is the closest course in this selection to the center of Austin and can be found just east of the 35 freeway. It has a driving range and usually pretty good greens (for a muni). Austin Munis only charge $3 for beers and even allow you to bring your own if you want to. Try to sneak over for a late afternoon round if you can. This is my home course, so it has a little place in my heart!
2) Plum Creek - 750 Kohlers Crossing
A course about 10 miles south of town is pretty darn good. It is part of a subdivision so you can see some Austin/San Antonio's growing population. The course is home to the Texas State Golf team, which means the practice facilities are solid and the greens are great. The entire course is pretty challenging and as an old man once told me, the 2nd hole from the tips is "the 6th longest hole in Texas"...so its got that going for it. Great course and not too far from town.
Another great Austin public course that is just north east of town. You can get to it pretty easily off of 290. As with most of these courses, the club house isn't much, but the course is legit. From the tips this course is really challenging, but every hole is fun and the greens are always in good condition. If you are staying a little north and want a good challenge for the right price, it's a great option.
Kizer is laid back Austin represented in a golf course. It's an Austin muni that is links style (kinda) and is not too challenging (unless the wind picks up, which it can). The course though is always in good shape and is perfect for a Friday round. The course is pretty flat so many times you will see a group of guys walking (or riding) the course with some music and some beers. And remember since its an Austin Muni, beers are pretty cheap or BYOB and the amazing sunsets are free!
Lastly, if you are wanting a little longer experience, check out Star Ranch. It is north of the city in a subdivision. The Saturday rate is more expensive than these other options, but you get a breakfast buffet, a lunch buffet!, cart, and range balls. The course is real good too. Think about it and check it out.