I can't speak from personal experience, but if I was looking at a Motel 6 or the like, I'd probably stay at the Motel 6 out by the airport. That's on the east side of town, but access to downtown is REALLY easy from the airport. 15 minutes on I-40 and you'll be in the heart of downtown. There are a lot of reasonable hotels on the east side of town that are nice, but affordable.
No matter what, do NOT stay in any hotels in the north central area of Nashville. The area looks okay in the day, but gets very questionable as the sun goes down. Avoid Dickerson Pike and Madison. However, further north, like Hendersonville and beyond would be fine.
There aren't a lot of hotels on the south side that are reasonable. When you get out to areas like Brentwood or Cool Springs, you run into where the business parks are. The hotels are nice, but pricey.
I'd avoid downtown just because anything worth staying in will get expensive quickly.
Anything near the airport (esp. on Stewarts Ferry Pike) should be good. If that doesn't work, then try the west side of Nashville, like Belleview, Kingston Springs, and further west.
Let me know if you have any spare time while you're here and would like to grab supper, get a few adult beverages, go shooting, etc. (not necessarily in that order).