Normally in this scenario I would ask my client if they are looking to rent or buy. There are many more choices if you are going to buy. All of these options(in your price range) I would estimate to be a minimum of 15 minutes from downtown Nashville.
As far as rentals go I would recommend Nashboro Village. The area is nice and fairly close to downtown (less than 10 miles). Also the cost of living is much lower than other areas of nashville (gas, food, etc.) I call this area the bang for your buck area. Your price will get you a spacious apartment meeting your specfications, with a fitness center included. They also have tennis courts and a golf course. If this area is not to your liking do not fret, there are many other areas available.
When it comes to buying a home it's much different. I would rather you personally investigate each home. There are many homes all over Nashville that the mortgage would be $800 or less. We would provide market analysis as well as personal insight to ensure that you made the best decision you could make.
Either way we are always available to answer any questions you may have. We strive to exceed our clients expectations and provide a hassle free environment. Call us anytime we look forward to hearing from you.
-Bailie and Paul