I think you are looking at a Sweetbay Magnolia - Magnolia virginiana.
Those are fine plants for southwest Virginia and northeast Tennessee - and a lot of other places in eastern North America. While they are native to wetter or swampier sites, they are perfectly well adapted to normal residential landscapes.
This plant blooms in June here with a lemony fragrant creamy white flower about 4 inches across, and quite prolifically. This a great plant to have near an outdoor seating area, especially if you can steer your downspouts toward it, where you can enjoy its appearance AND fragrance during summer months.
There are forms that are totally deciduous, and there are selected named varieties that hold their green leaves through the winter.