Nashville certainly is a cosmopolitan town. The city itself is a blue dot in a sea of red. The city has a vibrant music and arts scene, and not just country music. In non Covid times, you can find music any night of the week and Art walks several months out of the year. Nashville has so great restaurants as well. If you are into sports, the city has NFL and NHL, as well as MLS. Additionally, the symphony is incredible and has a beautiful concert hall and the Frist Center is a very nice art museum that hosts a variety of exhibits on rotation. There is always something going on.
Cost of living depends on what and where you are looking. We moved from New England and experienced a significant drop in the cost of living, but it could be higher depending on where you are moving from. As others have said, East Nashville is a great area but has a bit higher living cost because everyone wants to live there. There are other areas of town that are more affordable and offer their own benefits, and, despite traffic, once you learn your way around it's pretty accessible.
Happy to help answer any questions you might have.