Hi,

Most people in Austin wouldn't look twice if you washed your Vanagon in
your bathing suit. (Unless you were either very good looking and naked
or famous and naked.)

State parks have showers, and many will let you in towards the end of
the day "just to look around" for free. Of course, if they see you
every day, they may catch on. Otherwise, day admission charges are
inexpensive. There are quite a few people that go to Barton Springs
(Zilker Park), for no other reason than the (clean) fresh water with
free access. Public restrooms are nearby.

If you look like a student (carry a backpack), then you can roam around
the University of Texas un-noticed - the rec center is a good place for
a clean restroom, place to snooze in air conditioning, etc. This is a
very big university, and it is easy to blend in - many non-traditional
students. Probably most large universities are the same.

Conrad