What part of the state? What zone?

Inland sea oats is a great grass for shade/part shade and beautiful seed heads in the summer through winter.

Texas Gold Columbine (Aquiligia chrysantha) is lovely and grows around the LadyBird Wildflower center...

It's my favorite columbine.

Columbine (especially Aquilegia chrysantha, but also A. canadensis), American beautyberry (Callicarpa americana), wild blue/Lousiana phlox (Phlox divaricata), flowering dogwood (Cornus florida), Texas betony (Stachys coccinea), any of the yaupon hollies, southern wood/shield/whatever fern (Thelypteris kunthii/dryopteris normalis), Virginia sweetspire (Itea virginica - especially improved 'Henry' cultivars), and, a favorite, golden groundsel (Packera obovata). Zexmenia (Wedelia texana) works sun or shade, much like turk's cap.

Gregg's mistflower (Conoclinium greggii) also looks promising, but not enough experience with it in shade yet.

Horseherb (Calyptocarpus vialis) does well in shade where the rabbits can't reach it. Pigeonberry (Rivina humilis) and frogfruit (Phyla nodiflora) are nice, but seem to need more sun (or something) than we are giving them to thrive in our Dallas clay.

Oh... and a second for inland sea oats.