In a large bowl, toss the chopped tomatoes with the cucumbers, tomato juice, olive oil, lemon juice, onion and 3 tablespoons each of the basil and cilantro.
Working in batches, puree the vegetables in a blender.
Pour the soup into another large bowl, season with salt and pepper and refrigerate until chilled.
Meanwhile, in a small bowl, blend the goat cheese with the remaining 2 tablespoons each of basil and cilantro and season with salt and pepper.
In a small saucepan of boiling salted water, cook the sugar snaps until just tender, about 1 minute.
Drain and refresh under cold water, then pat dry and halve.
Ladle the soup into shallow bowls and spoon a dollop of herbed goat cheese into the center of each.
Garnish with the sugar snaps, cherry tomatoes, radishes and avocado and serve.