Agreed re: Holston Hills. I played it two years ago in a Mid-Am qualifier and still remember every hole. There are some tremendously difficult shots, but the challenge does not outweigh the fun factor. For courses closer to Nashville, you could try the Legends Club in Franklin, which has two courses by Kite/Cupp. Frankly, there are not alot of GCA-friendly courses in Nashville. The one that was probably the best was old Richland Country Club, where Amy Alcott won the 1981 Women's Open, which was a Ross with plenty of width and challenge. Alas, it was plowed under 15 years ago and the club moved to the suburbs where Nicklaus built a course.
Also agree re: Lookout, but HH is better, in my opinion. If you can get on Belle Meade, which is quite difficult, it is a fun layout as well. For public offerings, Harpeth Hills is decent, but the greens are usually somewhat lacking.