Recently went for a long weekend, the best thing we did by far was to catch a show at The Listening Room. For the ticketed shows, you can get a table and have brunch or dinner there during the show.
Also:
Brunch at Adele's (near a bunch of outdoor shopping if that's your thing)
Third Man Records - Jack White's studio and record store, you can book a tour
The Country Music Hall of Fame is ok, but there is a ton of space dedicated to crappy modern country artists. With kids I'd be afraid you'd bore them a bit.
The Dukes of Hazzard museum is in Nashville, but a bit of a haul, and once you get there it's really just a store filed with DoH merchandise from the 70s and some vehicles you can take your picture in.
Y'all can skip The Parthenon, or if you do go, it definitely isn't worth paying the fee to tour the inside.
I really didn't realize what a "Bachelorette Party" destination Nashville was before going. Everywhere you go, you will be surrounded by pedal pubs and flat trucks carrying drunk girs yelling "Whoooo!" from about 10am forward. Broadway area is a disaster.
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