Looks like one of the ligustrums

Definitely oakleaf hydrangea

Yes, Rivina humilis (Rouge Plant), thanks! I guess it is the same as this specimen, just more verdant due to being shaded. Some report the berries are edible, others claim they are somewhat poisonous to humans...

Blakrab, you have four similar-looking Plantago species in central Texas. It isn't P. helleri, because that has widely spreading hairs, mid-stem. It isn't P. patagonica, because that has linear-lanceolate bracts beneath the sepals. It may be wrightiana or hookeriana. If wrightiana, the leaf blades are glabrous on the upper surface. If hookeriana, leaf blades are woolly-pubescent on the upper surface. The leaf detail in the photos isn't good enough to lock this down, but leaves with woolly-pubescence usually have a gray cast, and yours are green. I agree with Floral - Plantago wrightiana is a good candidate.