It was known as Broad Street long time ago. There was an area known as “Auto Row” because of many auto shops, dealers and tires shop at the beginning of the 20th century. (para leer en español aquí)
In the 1930s, a lot of performers started playing near the river, but then the popularity of Broadway started to decline when the Grand Ole Opry left the (gorgeous) Ryman Auditorium in 1974. However, in the 90s, the Opry moved some shows back to the Ryman and Broadway is what we know today.
Today the area is known as “Honky Tonk Highway”, lots of bars with no covers, some of them with many floors to enjoy different entertainment, restaurants and stores (lot of boots stores btw). It might not be the typical local scene, but at least for 1 night of your visit, you need to walk around this area and enjoy 1 or more shows. And who knows… maybe you’ll run into someone famous performing few songs at one of those bars.
Here’s a short video during the day, walking around Broadway and you can listen music coming out of some bars by noon on a Sunday. (360º video, so you can move the image around)