Texas is a big state with five gardening regions. The gardening (grow) region is a key factor in choosing landscaping. Your best bet is to consult with a local gardening store about the best options for your areas.
The most popular choices are English Ivy, Mondo grass, Asian Jasmine, Liriope and Blue Shade. Ground covers are often used around or under trees where grass grows poorly or tree roots are exposed.
One of the most beautiful ground covers is the Texas state flower which is the Texas bluebonnet. Bluebonnets are wild flowers which will spread and completely cover large areas. They are absolutely gorgeous flowers and when their royal blue color saturates an area, it can be quite mesmerizing and relaxing to enjoy.