I'm a long-time Nashvillian, so I sort of held back in responding until a few others had a chance to post, as I always enjoy hearing what outsiders highlight about Nashville.
You likely know Nashville has been declared an IT City and is incredibly popular with visitors from around the world.
Many really good suggestions for Nashville have already been made. Definitely don't miss charming downtown Franklin (cute, adorable shops, historic architecture and some fun lunch spots). If you can get tickets to the Blue Bird Cafe, you will want to do that...we locals don't even try for the most part...but I see the lines regularly as I am out and about shopping in Green Hills....it's extremely popular!!
Don't know if you were a fan of the TV Show, Nashville, but you could drive by the house where the main star lived on the TV show (on Page Road in the Belle Meade area), if that is something of which you are a big fan.
The 12South area is EXTREMELY popular during the day and into the evenings. Lots of good, casual restaurants and some cute shops, including a new one owned by Reese Witherspoon (who also recently purchased a house on Glen Levin that will be redone). Gosh, there are so many homes by so many stars that many of us "just sort of know about" and many that are not on "homes of the stars tours." Ditto for top songwriters. And, it is not unusual to run into the mega stars while you are out and about or at the grocery.....they blend in, and we Nashvillians treat them as regular humans allowing them to live normal lives among us. I remember hearing from someone when they were in a car accident with Dolly Parton (who was so very nice and kind about it).
The Germantown area of Nashville (a historic area north of downtown) is also very popular with some old favorite restaurants and some new ones.
Google: styleblueprint.com which is a free newsletter that give top things to do in the city each month, new restaurants, reviews of some restaurants, highlights of chic hotels, along with fashion and home decorating tips. I "think" (not sure) there may also be a Memphis version, too.
I'm not personally a fan of Memphis, but there are those who love it. Ducks at The Peabody are among my fond memories of spending several years working in Memphis.
The Wall Street Journal did a weekend feature on 3 days in Nashville a few years ago. Google to find it.
Please feel free to share any of your group's special interests, or questions, and I will do my best to answer or provide advice. We are honored to have you select our city for a visit, and we hope you leave feeling the love we all have for Nashville. It is growing fast, and traffic can be challenging.
Where are you coming from?