Pemberton Heights is a pretty unique area. Unlike Clarksville which originally was economically depressed but over the years has become more pricey, Pemberton Heights has historically been well-to-do. One of the benefits of this is that it is easier to find a house that is decent square footage (from 1500-6000 square feet) without an awkward add-on because they were built originally with 3+ bedrooms and 2+ baths. Although many of the houses were built in the 1930's and 1940's, the neighborhood is very clean with well maintained houses and lawns.
One cool historical marker of Pemberton Heights is the Pemberton Castle. It pretty closely resembles a castle with mossy stone, a turret and round rooms, and it was built by a UT architect who lived there for a while. The surrounding homes are pretty awesome as well with decent lots and an average of 2800 square feet. The neighborhood is pretty close in to town, near the intersection of 24th and Lamar, which makes it extremely convenient to downtown, UT, Arboretum shopping, or pretty much anywhere. If you have not driven through the area, it is worth a look.