My favorite hamburger in Nashville - a blue cheese burger - is made at Bobbie's Dairy Dip. Mom treated us there, because she likes it *almost* as much as I do and because she is awesome. We also ate fries (yum!) and milkshakes. I likely got a James Brown. Chai & coffee & ice cream? Yes, yes!
If you decide to visit, be forewarned that Bobbie's is in the ghetto, you'll be sitting on picnic tables, there are no bathroom facilities, and you have to stay outside. But, the burger! Totally worth it!