I love to ride my bicycle on the Shelby Bottoms Greenway. Entirely paved and with very little elevation change, the greenway is not particularly physically demanding, but very rewarding. It is indeed green, with a rural feel in the middle of a major city.
I like to start in Two Rivers Park, where another greenway's trailhead is located just off of McGavock Pike. It's about 1.5 miles to the Cumberland River, and on this side of the river, the terrain is a bit hilly. After crossing a really nice pedestrian bridge, from which you can see the Opryland area with its big riverboat, you begin the Shelby Bottoms Greenway. You can go north around the loop and come back to the bridge, or go south immediately, which is what I usually do. This trail runs along the Cumberland River and ends at the south end of Shelby Park. The Nature Center in the park is nice and has restrooms available. I usually continue south from the park, riding on Davidson Street's bike lane, to LP Stadium (home of the NFL's Tennessee Titans), a distance of about 2 miles. From there, you can go across another pedestrian bridge, or go over to the new Cumberland Park, to the left of the bridge.
An interesting side trip is to take the trail from the river toward the Shadow Lane Trailhead. Just before you get to the trailhead, you will pass a trail that leads to the old Cornelia Fort Airport, which is now closed as an airport and owned by the city of Nashville. Ride up and down the long runway and pretend you're about to take off! Cornelia Fort, by the way, was a female pilot who delivered warplanes to the Army Air Corps during WWII and was killed in a crash.
Total mileage for the round trip I've described is about 18 miles.