Lower Broadway does not have a dress code, but a few practical choices will make the night a lot better. Here is the honest version, without the catalog-style advice.
The honest answer: it is casual
The honky-tonks on Broadway have no dress code. You can wear essentially whatever you want, and you will see the full range, from full western outfits to jeans and a t-shirt to bachelorette-party costumes. You do not need boots or a cowboy hat to fit in. Plenty of people wear them, plenty do not, and nobody is checking.
Shoes matter more than anything else
This is the one thing worth getting right. You will be walking the strip and standing in crowded bars for hours, often on floors that have had a few drinks spilled on them. Wear comfortable, closed-toe shoes you can last a full night in. Brand-new white sneakers will not stay white, and heels you cannot stand in for five hours will end the night early.
Dress for the season, because Nashville commits to it
Summers are hot and genuinely humid, so go light, and remember the rooftops have no shade. Winters are cold, and you will be moving in and out of bars all night, so bring a layer you do not mind carrying. Spring and fall are mild by day but cool off after dark, so a jacket is worth having.
Where you might dress up slightly
A handful of venues lean a little more polished. The supper clubs and cocktail rooms, like Skull’s Rainbow Room, Sinatra Bar and Lounge, and Blueprint Underground, suit smart-casual better than shorts and a tank top. None of them enforce a strict code, but you will feel more in place dressed up a notch.
Keep it light
Carry as little as possible. A small bag or no bag is easier in packed rooms than a backpack. Assume a drink will get spilled near you at some point. And since a Broadway night runs long, going out with a full phone battery is worth more than any outfit choice.