Nashville has no shortage of hotels so you can certainly find your own. But if you want to be in the general vicinity of Deer Run, we recommend the following:
Holiday Inn Express Spring Hill (approximately 15 minutes from Deer Run)
Hampton Inn Spring Hill (approximately 15 minutes from Deer Run)
Drury Inn Cool Springs (approximately 25 minutes from Deer Run)
A Loft Cool Springs (approximately 25 minutes from Deer Run)