My friend lives in Nashville, but haven't been there since getting into the beer thing a few years ago.
Anyway, google maps is your friend. I looked up the Ryman, searched nearby for "brew", and looks like you are in luck. About 3 breweries or beer-bars nearby... you can look into these further.
Big River Grille and Brewing, Broadway Brewhouse Downtown are closest - Broadway got better ratings. Yazoo brewing looks like its within a little drive or cab ride or maybe even hike.
More came up as well but does not appear they are as close...