When friends and family come in to town, we get a feel for what they might like to see and/or do with a short interview and conversation of what they've heard of Nashville already or preferences for spending time.
Feel free to post again some activities you enjoy (sites, social activities, food, walks, concerts) and we can hone down the answer.
I've included a few stops we almost always recommend, things that might fall under the, "Oh, you went to Nashville, did you see the…"
The Grand Ole Opry is a little drive outside of the city (20 min), but quite worth it to say that you've been there (a concert is a bonus but not necessarily required). You can walk around the premises of the Opry House for free but will need a ticket to get inside past the Gift Shop.
If you leave your car in the Grand Ole Opry parking lot, you can take a short walk to the Gaylord Opryland Resort . "A hotel?" you may ask. I know, it's a little strange for this to be a recommendation, but depending on personality of the visitors, it's a uniquely-huge hotel/building with indoor gardens, a little history of all things "Opry" (roots of country music/bluegrass) and is semi-worth strolling through for 45 min while in the area (it's an easy loop through the hotel).
Keeping with the music sites and everything 'Music City', we recommend the Ryman Auditorium back in downtown Nashville, which was the original Grand Ole Opry House (still has the pews inside). Look up the Ryman – it's a "can't miss" if you like that sort of thing.
Of course, once you are back downtown near the Ryman, you'll be right along Broadway. If you get a parking spot on the street or one of the garages, plan on time to join the crowds, walk Broadway, and step inside the many restaurants/businesses that almost all have live music in the evenings and especially on the weekend. Also along Broadway opposite direction to the river is Bridgestone Arena , where Nashville's hockey team (the Predators) plays and concerts/events of all sizes are held. There might be something going on the weekend you are here.
Also downtown is the crazy huge new Music City Center – wow.
If you like Country Music, the Country Music Hall of Fame might be up your alley. It is also downtown (paid entrance fee).
If you've had friends who went to Vanderbilt University or Belmont University , and even if you haven't, those two Universities are less than 1 mile apart (5 min south of downtown) and might be another, "Yeah, I drove by and saw where those were." Vanderbilt is known for it's medical efforts (amongst other achievements) and Belmont for it's School of Music and Music Business (being on the end of Music Row which houses companies like Sony Music, Word, ASCAP, SESAC, etc and recording studios like Historic RCA Studio B , etc.). The Belmont Mansion is on Belmont's campus if you like historical houses.
It seems that the Bluebird Cafe (south of the city about 8 min) is highly popular for visitors to Nashville. Lots of songwriters perform in a small space and tell the stories behind the songs heard on the radio. There's usually a line out the door, so look into it online and see if you can get reservations.
The Station Inn is always a stop for classic sounds of Nashville.
On the more formal side, the Schermerhorn Symphony Center gives regular concerts and has a beautiful building with supporting acoustics.
Food is a cool aspect of Nashville, which I imagine is not unique to the city, but is definitely something the city can enjoy and be proud of.
You'll find local businesses like Fido (coffee shop atmosphere), the Pancake Pantry (make your own pancakes with just about anything; breakfast or otherwise), and Puckett's Grocery & Restaurant (meat & threes) thriving to young crowds and old.
There are too many good spots to mention. Loveless Cafe (it's kind of a drive, but people seem to like to go there), Gabby's Burgers and Fries (check their operating hours), Sweet Cece's (for frozen yogurt) and Jeni's Splendid Ice Creams in East Nashville (up-and-coming/trendy(?) restaurants) are meals we have enjoyed. See my note below about other places online to check out restaurants and see which others you might like. That doesn't even include the many places to eat in Franklin , about 25 min south of Nashville. If there is time and interest, we almost 100% of the time bring family/friends down to Franklin.
Depending on preference, there are a few parks/bits of nature to enjoy around the city of Nashville as well.
First on our list is the Radnor Lake Natural Area and Wildlife Refuge . About 10min south of the city, you can park your car in the free lot and walk 45min-1hr on nature trails around the lake. This can be a highlight in the fall with good weather and is beautiful in the spring, too. Deer, turtles, and other critters are regularly seen.
Also of note is Percy Warner Park , about 10 min from Radnor more southwest of the city. You'll find consistently favorable reviews of Percy Warner.
Not far from Edwin & Percy Warner Parks is Cheekwood Botanical Gardens and Museum of Art . Not everybody's style to visit when coming to Nashville, but if you like that sort of thing, it's beautiful grounds and southern feel are memorable. Check the seasonal updates. If you like art, the Frist Center for The Visual Arts is Nashville's Art Museum, which is downtown, and if you've got the time (35 min drive) Leiper's Fork is worth visiting with art galleries for fine art and hand-made. It's a funky and dare I say "Historic" village. Look up the Natchez Trace and see if it interests you.
Lastly, for things to do outside, make a stop by Centennial Park on West End. Back in 1897 they built the Parthenon , a literal replica of the one in Athens without the expensive marble. It won't change your life, but I recall thinking, "They what?" when I heard there was a replica here. It will give you an idea of what the one over in Greece is like if you haven't been there. It is also a nice stroll around the park and lake if you care to take the time.
Finally, let me just say that there is a plethora of information and planning tools to help with your visit should you want to gather from other sources, including the more official, "marketing" side like like Nashville's own Tourism website "Visit Music City". Another is, of course, the ever-steady reviews and recommendations on TripAdvisor .
We are happy to write answers here on trippy because it's a growing place to get answers and start conversations for travel around the globe. I hope your planning fuels your desire to make the trip!