Matt:
My grad school roommate grew up playing at Belle Meade and I had the chance to play it a couple of times while living in Nashville. Its a pretty fun course with a good mix of holes (some long par 3's, short par 4's, etc.) and is kept in great condition. I wouldn't describe the property as the best I've seen for golf, but there is a bit of elevation. On the whole, any up or down movement is pretty gradual. There are a couple of holes that are across one of the bordering roads, requiring a crossing to get to. The clubhouse is very old school, with a great men's grill that could cause many a golfer to miss the dinner bell.
Located in the heart of a very old and established neighborhood, its no surprise that the club is considered exclusive. Its probably had the same family names on its roster since its inception.
Sven