Ask Mr. Smarty Plants

"Although trees are generally divided into two groups by root type—tap root trees (such as oaks, hickory, walnut, conifers) and lateral, or fibrous, root trees (maples, ash, cottonwood)—this distinction is most evident as seedlings or saplings. Once the tree is planted and begins to mature, the distinctions between the root types become less pronounced. Then, the depth and lateralness of the roots is greatly dependent on the soil condition. Highly compacted soils, soils with low oxygen content and soils where the water table is near the surface are not likely to produce a strong tap root. Their roots are more likely to be lateral and located very near the surface with the majority of the roots located in the top 12 inches of soil. Also, it is important to realize that the spread of the roots can be at least 2 to 4 times greater than the drip line of the branches.

You can read the recommendations from Iowa State University Extension Service for Sidewalks and Trees which bases the distance trees should be planted near pavement on the mature height of the tree. Their recommendations are:

1. trees with a mature height of less than 30 feet, 3-4 feet from pavement,
2. trees with a mature height of 30 to 50 feet, 5-6 feet from pavement,
3. trees with a mature height of greater than 50 feet, at least 8 feet from pavement.

You could consider installing some sort of root barrier between the tree and the wall.  Here is more information about root barriers."

Here are some large shade trees that are considered tap root trees that are recommended for Harris County:

Quercus macrocarpa (bur oak) and more information

Juglans nigra (black walnut) and more information

Carya illinoinensis (pecan) and more information

Ostrya virginiana (hophornbeam) and more information

Quercus virginiana (live oak) and more information

Quercus alba (white oak) and more information

You can use the Texas Forest Service Texas Tree Planting Guide to select other trees according to your own criteria.

Quercus macrocarpa

Juglans nigra

Carya illinoinensis

Ostrya virginiana

Quercus virginiana

Quercus alba