Another way to research this topic would be to take a look at changing demographics. This site is great for that: http://projects.nytimes.com/census/2010/map
Personally I see great things happening among the majority of our affordable urban neighborhoods. You may have to be a bit of a pioneer, but I'd feel confident investing in Shelby Village or Inglewood. Also, you should look to the west of Gallatin Pk. See 37207: http://www.tennessean.com/apps/pbcs.dll/article?AID=20123112
Also, I'd look towards Woodbine/Flat Rock, Buena Vista, Croleywood, & Donelson. You can't put a price on convenience.
Finally, my site linked below might help a little.
My best advice is to try to beat the crowd. I bought on the south side of Shelby back in 2004 and people thought I was crazy. The people who started renovating in Cleveland Park were completely out of their minds and on the wrong side of Gallatin Rd people thought. It really is block by block in East Nashville from Shelby Village all the way to Inglewood. You also need to take into consideration how long it'll take the rest of the block to catch up. The neighbors are a factor in buyers' decisions.
If you have your areas pretty well pinpointed I can map the comps and we could really analyze the data for the particular areas you're considering.
I will be happy to show properties in any area of Davidson County.