Okay. Nashville is a total mixed bag in the city--unlike any place I've ever lived!-- you can have $500,000 homes next door to crack houses in many of the neighborhoods.
Lots of people love East Nashville. It is very trendy and hip. Also becoming more and more pricey but there are still some okay values if you don't mind doing a little reno. (Will you be buying or renting?)
Personally, I would not feel comfortable living in Antioch. It is probably the most affordable area but it has a high crime rate for my taste.
Madison also has a higher crime rate but feels "safer" for some reason.
The Donelson/Hermitage/Mt. Juliet area is very suburb. You'll need a car to safely get anywhere (due to lack of sidewalks) but it is reasonably priced.
Hillsboro Village is way expensive--dh's rent (650 sq ft) was more than my mortgage (1200 sq ft) but easily navigated by foot.
North Nashville has some nice places at fair cost but again has the super mixed neighborhood problem of really nice homes next to condemned homes.
Feel free to PM me for more info...welcome to the friendliest city in the US!