In a small bowl, combine the chopped tomatoes, chopped fresh basil and red wine vinegar. Season the mixture to taste with salt and pepper. Set aside.
Preheat the grill to medium-high heat (or preheat broiler). Brush 6 eggplant slices lightly with olive oil (reserve the remaining eggplant for another use). Brush the bread lightly with olive oil. Grill the eggplant and bread until golden, about 4 minutes per side for eggplant and 2 minutes per side for bread.
Arrange the bread slices on plates. Spread the goat cheese on top, dividing evenly. Top with the eggplant slices and season with salt and pepper. Using a slotted spoon, mound the tomato mixture on the eggplant, spread to cover and serve.