royallmonarch and hughes already covered some of the best spots so this will be supplemental.
Mainstream Music Venues:
The Basement - both locations host big acts but also locals
Brooklyn Bowl - not homegrown, but still a nice venue
Robert's Western World - if you must visit a honky-tonk, might as well visit the original
Coffee:
Crema - homegrown classic
Sump - not homegrown, but may have the best espresso in town
Headquarters - cozy spot
Food:
Kisser - Japanese, award winning, lunch only.
S.S. Gai - Thai grilled chicken and sticky rice. Tastes like my childhood.
Red Headed Stranger - Tex-mex, best flour tortillas in town.
Mother's Ruin - Good burger, great fries, amazing brussel sprouts.
Deg Thai - Not the only great Thai spot, but one of the best.
Little Hats - Italian deli and market. Get the Chicago style beef, dipped.
Gabbys Burgers and Fries - Best burger in town, lunch only.
Nicolettos - Handmade pasta with a mean meatball sub. Right next to Mickey's Tavern and they don't mind you bringing in Nicolettos to go with your beer.
Drinks:
Rice Vice - Sake, sochu, and beer. My favorite spot.
Attaboy - Cocktails. No menu. Expensive, but a good experience.
Martha My Dear - Good cocktails. Chill.
Honeytree - Mead if you want to try it. Bad Luck Burger is also here and worth a visit.
Never Never - Great bar with a great Mexican food truck. Lots of neat places nearby.
Otto's Bar - Sister spot to Headquarters. Tacos and drinks.
Random Distractions:
Nashville Zoo - great zoo and zoolumination is running all winter.
Grimey's, Anaconda, Living Waters - Records, vintage, coffee, and beer all in one spot.
Tempered - Chocolatier shop. Truffles, hot chocolate, espresso. Bonus: converts into an absinthe bar at night called Green Hour.