Green Wood in Gallatin, TN Green Wood is The affordable community in Gallatin, Tennessee, that finally has all of the things on your must-have list that you've been looking for! Everything about Green Wood Apartments and Townhomes portrays the quality of the community, the design of the apartment homes, and the care with which the members of the management team undertake their responsibilities. Our pet-friendly community is located just minutes from shopping, dining, and entertainment with quick access to major highways and downtown Nashville. The sought-after three bedroom townhome and garden apartment homes at Green Wood include washer and dryer connections, huge eat-in kitchens, and private patios with extra storage.