If you have some spare time, and don't mind driving, I'd recommend driving the Natchez Trace Parkway from where it starts near the Loveless Cafe (somewhere you should really really eat breakfast) down to Leiper's Fork. Stop in at Puckett's Grocery (also a restaurant) for some barbecue, and then drive back along Old Hillsboro into town.
Also, if you like outdoors stuff, then on the way back make a detour to Radnor Lake and hike to or around the lake.
If you're a country fan, you may want to stick closer to downtown, and see if you can tour the Ryman Auditorium, and get in the Country Music Hall of Fame. In that case, you should still make the trip to the Loveless Cafe on Friday for breakfast. It's a pretty drive to get there, and you may even eat enough to not have to worry about lunch.