I wouldn't at all be surprised to see the first Supercharger at or around the Brentwood service center location. Lots of stuff in the Cool Springs area, it's on the far south side of town, they have a partnership in place with CBL who owns Cool Springs Galleria nearby. Seems like an ideal spot.
Selfishly, if they're going to do a second Supercharger in the area I'd love for it to be on the north side of town, either on 65N or 24W. I do a lot of traveling up towards Kentucky and a Supercharger in that general vicinity would be helpful.
(Hell, Tesla, if you're listening, put one in Clarksville, TN to make the I24 corridor more do-able for Tesla owners. Or at least for me!)