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."

Because of the small size of your space, I will suggest several smaller trees.  Here are some trees that have a maximum height of 30 feet or less:

Cotinus obovatus (American smoketree).  Here is more information.

Frangula caroliniana [syn. = Rhamnus caroliniana] (Carolina buckthorn).  Here is more information.

Cercis canadensis (eastern redbud) has a rapid growth rate of 15 to 30 feet.  Here is more information. 

Viburnum rufidulum (rusty blackhaw).  Here is more information.

Ilex vomitoria (yaupon).  Here is more information.

You might be able to get away with smaller medium-sized trees.  All of these next ones would be considered medium-sized or small trees with a maximum height of less than 50 feet.

Fraxinus texensis (Texas ash)  has a rapid growth rate and is long-lived, 30 to 45 feet.  It  also has beautiful fall foliage.  Here is  more information.

Acer grandidentatum (bigtooth maple) has both a tap root system and lateral roots, a moderate growth rate up to 50 feet and beautiful fall foliage.  Here is more information.

Quercus laceyi [syn. = Q. glaucoides] (Lacey oak).  Here is more information.

Cotinus obovatus

Frangula caroliniana

Cercis canadensis

Viburnum rufidulum

Ilex vomitoria

Fraxinus texensis

Acer grandidentatum

Quercus laceyi