The photo for this postcard was taken in the mid-50s, as far as I can tell.
It’s still there, more or less, but it’s for sale as of the date of this posting.  In the 1959 City Directory, this motel is listed as being owned by Esther D. and Pratt A. Hegler.

On the front: (in a cursive typeface) Greenwood Motel
(sanserif) 1840 Ft. Henry Drive KINGSPORT, TENNESSEE

On the back:

(the first part is the same as on the front)

Phone CI 6-6187
On U. S. 11W – 23 Hwys.
-Kingsport’s Most Luxurious Motel –
Beautyrest Mattresses – Ceramic Tile Baths with Tubs and Showers –
Air Conditioned – Room Phones – Free 21″ TV – Wall to Wall Carpet –
Electric Heat- Room Thermostats – Shaded Grounds – Children’s Swings – Picnic Table

The card is a TichnorGloss QUALITY VIEWS. REG. U. S. PAT. OFF. MADE ONLY BY TICHNOR BROS. INC. BOSTON 15 MASS.

Plate number is G89859