Place potatoes in a large saucepan; cover with water. Bring to a boil. Reduce heat, and simmer 15 minutes or until tender; drain. Cool slightly; cut into 1 1/2-inch chunks. Place in a large bowl; toss with vinegar and 1/4 teaspoon salt. Cool completely.
Combine tomatoes, olives, basil, oil, and garlic. Add olive mixture, pepper, and remaining 1/4 teaspoon salt to potatoes; toss gently to combine.