Check out the Nashville Harriers. They have a Facebook page you can use to make contact. It's a fast group and the Tuesday night workouts are usually held at USN's "River Campus," i.e., a sports field facility about ten minutes from the downtown arena just off Briley Parkway.
There are several greenways where you can get in a long run as long as you don't might asphalt. There are several groups that do organized runs throughout the week. Check out the Nashville Striders, the Nashville Running Company, Fleet Feet, and Rhythm Running for more information. Percy Warner Park has some great hills on its 11.2 mile loop. There is also a shorter 5.8 mile loop. There are also some dirt trails at Percy Warner, but they are technical, single track... not much use for a 2:45 marathoner. It pains me that Nashville has no fast, dirt trails wide enough to a group tempo run, but there has been no interest in creating one.
One little-known resource is Vanderbilt's indoor 300-meter track. For $45/month, you can join Vandy's Wellness Center and have access to their full gym facilities, weights, treadmills, spin bikes, indoor pool, outdoor track, climbing wall, basketball courts, and most importantly, a wide-turn 300m 6-lane indoor track. I ran there today.
Nashville has one major adult track meet... the Music City Distance Carnival in June. It attracts a few national caliber athletes every year and is a fun, night event.
The weather here is mostly great, especially compared to places like Chicago. Nashville is literally transforming in front of our eyes. New upscale housing is going up everywhere near downtown. We have award-winning craft beers, restaurants of all types, and a music-oriented downtown nightlife. It's a fun place to live and to run.