In that case you sort of have your choice of chain restaurants. That hotel is just the other side of I-65 from the mall. There are more independent restaurants in the area than there used to be, but I don't think most of them would be a good spot for a teenage baseball team. :D I can't tell you exactly which of the chain restaurants might have private rooms, but I know that there is both a Carrabba's and an Amerigo in the area, and their locations elsewhere in Nashville have private rooms. Some other options to check out would be Famous Dave's and Las Palmas.
27 S Lafayette Ave, Brownsville, TN 38012
Ain't Mexican and I'm not sure about a big group but check em out.
Puckett's Grocery & Restaurant @ 120 4th Ave. S., Franklin, TN. 615 - 794 - 5527. *
One Stop Cafe @ 901 Columbia Ave., Frankin, TN. 615 - 794 - 3881. *
Willie B's Gourmet Smokehouse @ Franklin, TN. 615 - 595 - 6499.
120 4th Ave S, Franklin, TN 37064
One Stop Cafe
901 Columbia Ave, Franklin, TN 37064