Well, unfortunately it's a little too cold in winter for most of those to grow in the ground here. The summers can get too dry and intense for them to do well unprotected in the hottest months as well. I have Meyer lemon, Mexican limes and several different varieties of oranges. Mine come out of the greenhouse in Spring after last frost and stay on my back porch where they get about 6-8 hours of sun and get water daily. I get good fruit from all of them. Out in the yard I have native pecans, 4 varieties of apples, 2 varieties of pears, and peaches. I have two apricot trees that were 10 years old when I put them in 10 years ago, so they are 20 years old now and have yet to set fruit. I've had no luck with berry bushes except for the blueberries which are in containers as the deer and other wildlife eat blackberry and raspberry canes to the ground.

Most of the nurseries will carry a variety of fruit and nut trees. I always seem to find the citrus trees at the big hardware/home improvement type stores.

As for bananas, I'm not sure. One of the guys who is coming to the Ft. Worth swap next weekend says he has one to trade. I don't know how well they do here, but I see a lot of palm type trees in containers in peoples yards, but I've never seen one with bananas on it. Maybe osmeone else here has more information about them.
Cheryl

My Pomegranates made it through last year's record cold in San Antonio so I think they would work okay in Austin. They had been in the ground for a year so they were well established. No blooms or fruit this year, but many Poms in the neighborhood do have fruit and mine are still young.

You can probably grow banana trees, but will rarely get fruit unless you have a greenhouse because they die back each year. Mine are in a container and are protected during freezes and they still die back.

Roselee has posted about her Papaya tree and I think it needs a very mild winter to fruit also. If she sees this, she'll let you know.

For citrus, you will need a very hardy type and there are some available. I have one called "Lemon Drop" that made it through last winter but did not fruit this year.

Many trees sold at the large home improvement stores are not meant for our climate. Winters here are usually mild, but every once in a while they are very cold like last year so you have to keep that in mind.

The best reference for what works is Fanick Nursery here in San Antonio. You can also try some of the locally owned nurseries in Austin like The Natural Gardener for good local info.

Here is a link that might be useful: Fanick's