Ask Mr. Smarty Plants

There are several suggestions for native Texas plants to give your yard a tropical look. For instance, you might consider:

Palmetto (Sabal minor),
Texas palm (S. mexicana),
Spanish dagger (Yucca treculeana),
ferns such as cinnamon fern (Osmunda cinnamomea), and
heartleaf hibiscus (Hibiscus martianus).

We wouldn't really recommend Bird-of-paradise (Strelitzia reginae) for Austin since it is non-native (from South Africa), but also because we are too far north and too dry for it. A hard winter would do it in. Austin's summers are probably just as big a problem for many non-native tropical plants as its winters. Our summers are so hot and dry that many tropical plants succumb to desiccation. Likewise, our winters are not usually very humid so that desiccation, as well as freezing, are problems for evergreen tropicals. The tropical look you are trying to achieve will require more maintenance and resources if you use non-native tropical plants.

You might try visiting some of the better (locally-owned) garden centers in the area. The tropical look is popular and the Austin garden centers are used to accommodating such requests and stock plants, both native and non-native, for that specific purpose. You can find a list of native plant nurseries in Texas on the Wildflower Center web page and Native Plant and Seed Sources for Texas from the Texas Parks & Wildlife web page.

Finally, If you were interested in creating a water garden, you would have a number of choices for "tropical-looking" native plants. For instance, you could consider:

pickerel weed (Pontederia cordata),
one of the Texas arrowheads, such as duck-potato (Sagittaria latifolia),
one of the Texas horsetails, such as field horsetail (Equisetum arvense),
water lilies, such as American water lily (Nympaea odorata) or the yellow water lotus (Nelumbo lutea),
and larger plants such as marshmallow hibiscus

The Austin Pond Society web page has links to regional water gardening nurseries where you might find these recommended native plants.