Ask Mr. Smarty Plants

Before we begin to answer your question, let's talk about "near".  There has been a great deal of  damage done to concrete patios, foundations, sidewalks and tree roots because a "small" tree grew up to be a big tree, with extensive roots. Concrete and paving do not mix well with tree roots; the paving can starve the tree of oxygen or water and the tree roots can crack the paving. We have extracted some material from this Previous answer for someone who needed to pave near existing trees.

"The ground area at the outside edge of the canopy, referred to as the dripline, is especially important. The tree obtains most of its surface water here, and conducts an important exchange of air and other gases. Any change in the level of soil around a tree can have a negative impact. The most critical area lies within 6 to 10 feet of the trunk. No soil should be added or scraped away from that area.

Paving should be kept out of the dripline and no closer than 15 feet from the tree trunk. If at all possible, use a porous paving material such as brick with sand joints, open bricks, bark, gravel, etc., which will allow some water penetration and gas exchange. Even with porous paving, the area around the trunk-at least a 10 foot radius-should be natural and uncovered."

This, of course, was telling them where to put the paving; in your case, you need to decide where to put the tree, since your patio is already there. We will make some suggestions for attractive trees for your patio area, but you will have to make the decision on where to plant your tree based on projected speed of growth and mature size, width of canopy, etc. You didn't say if you wanted shade or attractive foliage and flowers or a privacy shield, so we will pick several trees that would fill one or more of those purposes. We will go to our Recommended Species section, click on Tennessee on the map, which will take us to a list of 121 plants native to Tennessee. Click on NARROW YOUR SEARCH, click on "trees" under Habit, and the Narrow your search box at the bottom of the page. This will give you 52 trees native to Tennessee. Clicking on each scientific name will link you to our webpage on that plant, with more information, and you can go down that page to a link with Google. After you have looked at our list and studied the webpages, you can make your own list, and this time click on Light Requirements and Soil Moisture to match the conditions in your garden.

Cercis canadensis (eastern redbud) - 15 to 30 ft. tall, deciduous, blooms pink March to May, attractive foliage and flowers, needs part shade (2-6 hours sun a day) to shade (less than 2 hours of sun a day).

Chionanthus virginicus (white fringetree) - 15 to 30 ft., deciduous, white blooms April to May, part shade

Diospyros virginiana (common persimmon) - 36 to 72 ft., deciduous, orange edible fruit attracts wildlife

Fagus grandifolia (American beech) - 50 to 80 ft., fall color persistant into winter, good shade tree, bears edible beechnuts, important food for wildlife

Ilex opaca (American holly) - 25 to 60 ft., evergreen, bright red berries on females, must be a male within 30 to 40 feet for production of berries, attracts songbirds, slow growing

Nyssa sylvatica (blackgum) - 30 to 60 ft., falll color, shade and ornamental, honey plant, fruit consumed by birds and mammals

Platanus occidentalis (American sycamore) - 75 to 100 ft., deciduous, wide canopy, shade tree, attractive bark

Taxodium distichum (bald cypress) - 50 to 75 ft., exfoliating red-brown to silver bark, deciduous conifer

Cercis canadensis

Chionanthus virginicus

Diospyros virginiana

Fagus grandifolia

Ilex opaca

Nyssa sylvatica

Platanus occidentalis

Taxodium distichum