I live in Nashville, will try not to echo things others have said...
Hotels:
Prepare your wallet... places that are a little bit cheaper could be along West End Ave (There's a few Marriott brands, a Double Tree and a Hilton Garden Inn in Midtown). Still super close to Broadway and a bit quieter for getting some sleep too.
There's an Extended Stay America that may be closer to a residence inn near 440 / West End if you wanted to try that to save some $.
The JW Marriott, Westin or Omni probably the nicest in downtown area if $ grows on your trees.
Activities:
Definitely find a show at the Ryman. Awesome experience.
Had a friend come for work one time and they did a riverboat for a dinner cruise. TBD on if that would be your speed. Food probably forgettable.
The Frist Art Museum usually has some cool rotating exhibits. One time they had a classic car one, and one time there was an Art Deco style / design exhibit that I missed. Close to downtown, so you could be downtown without Broadway-ing
Preds Hockey - someone else mentioned, but it's a lot of fun. You don't have to be a big hockey fan to go, and it's WAY better live than it is on TV
Goo Goo Cluster Factory - candy shop where you can make your own Goo Goo Cluster
Country Music Hall of Fame - If you don't go into the museum itself (lots of "old country", less new "bro country" thank goodness), definitely poke your head in to check out Hatch Show Print. They make a bunch of old letterpress prints that are neat to look at. Make sure you go check out the "art gallery" closer to 4th avenue too, not just the storefront area (art gallery has larger format, more $$$ art that's neat to look at; storefront has smaller, think 11x17" type, prints with things that are more souvenirs)
If wives / GFs coming with, they'll probably enjoy a day shopping the girly boutiques in 12 South area.
Food:
Downtown/close: mostly forgettable, but there are some places to check out...
Someone mentioned D'Andrews... not far from my office and a very solid breakfast / lunch spot
There's a Puckett's downtown (southern / meat n 3 type)
Arnolds (better meat n 3)
Kayne Prime (if you want to go $$$$ on a steakhouse, this is your spot)
12 South:
Embers Ski Lodge has great wings
Buttermilk Ranch is the "new" pancake pantry and can have a shorter line
Five Daughters bakery has "cronuts" (think a cross between the layers of a croissant and donut; has fillings)
Urban Grub (grill / a touch fancier)
East Nashville:
Others mentioned Butcher and Bee. Really Good.
I also like Red Headed Stranger for tacos (more Tex-mex style... really really good Tortillas)
Joyland is Sean Brock's fast casual burger / diner like concept that's really good and reasonably priced / faster.
People rave about Pharmacy burger and Mas Taco... the food is okay, but the ambiance when the weather is nice are the real sellers.
I personally don't love 5 points pizza, but you'll hear some people suggest. If going for pizza, go to Roberta's at Urban Cowboy Public House in East. Really good pizza and a cool bar. Get the pepperoni rolls with your pizza because they are delish.
Other options:
L&L Market on Charlotte has a little brewery, a conveyor charcuterie belt place for the ladies, and Penne Pazze for some really good Italian food.
Other Italian that's a little off the beaten trail would be Coco's Italian Market on 51st Ave and Pastaria in One City (Charlotte Ave just inside of 440)
If you need a good cheap meal, McDougal's Chicken fingers is just outside of downtown on 12th Ave S and really good.
BBQ ideas:
Others have mentioned Martins, and they are indeed State supporters. Have a '21 Natty banner in the location downtown. Really like their Ribs at Martins
Peg Leg Porker will have a long line, but generally worth the wait. Ribs or Pork sando here.
Shotgun Willie's is on my list as it's a TX style brisket place, but it's only open lunch hours. Everyone raves about it.
Central BBQ has a location near Vandy if you have been in Memphis and want their stuff again. Good, but not a true "Nashville" pick...
Edley's has multiple locations and is your best all-rounder type player. The turkey is phenomenal, the brisket tacos are a hit and my personal favorite is the Kermit pork sandwich (topped with a few fried pickles and some jalapeno ranch). Definitely get the banana pudding as one of your two sides here. Won't regret it!