In a blender or food processor, combine chopped tomatoes, cucumber, red and green bell peppers, red onion, and garlic.
Pulse the vegetables until they are finely chopped but not completely pureed.
Transfer the vegetable mixture to a large bowl.
Add tomato juice, red wine vinegar, olive oil, salt, black pepper, sugar (if using), and cayenne pepper (if using).
Stir the mixture well to combine all the ingredients thoroughly.
Cover the bowl and refrigerate for at least 2 hours or until well-chilled.
Before serving, taste and adjust the seasoning if needed.
Serve the gazpacho cold, garnished with fresh basil or cilantro if desired.