To answer the original question, there are several options and levels of discretion.
I was paranoid about giong to Waller the first time, but it's a clinic. So, people go there for other treatment. Test results come back within 10 days usually and you call to check your results. The basic gambit of tests are done there, but not much on the results except positive/negative. Your information must be provided there to get your results. So while it may be discrete, your information is on record there.
It's like $20 or less for STD test suite. Bring a book, lots of people in the waiting room so make sure you schedule enough time.
Planned Parenthood is another option. It's a bit pricier at $125 (I recall, it may not be correct) for general STD test suite. I think your information is also kept there.
I now use Any Test Now which has two locations in Austin and the north location was mentioned previously in this thread near 2222 and Mopac.
http://maps.google.com/maps?q=any+te...75.322266&z=12
AnyTestNow.com for some info, but links are broken and not much maintenance with their website.
It's about $200 for a full STD test sweep (maybe 180). It is completely anonymous (when paying cash) and no information is required. I use different names, like Don Johnson or Willy Bigg. Test results are ready within a week and you can pick it up at the store location. A report of detection rate and criteria for positive and negative are given.
If you have a good paying job, then most likely you have health care provider options. It is also an option, but a lot of information is disclosed so not very discrete from a paper perspective.
Ask your friends for a private practitioner recommendation if you don't know any personally.
It's good to have a health check frequently, especially in this type of lifestyle.