Cut iceberg lettuce lengthwise through core into 6 equal wedges. Also cut radicchio lengthwise into 6 equal wedges. Rinse and drain greens. Arrange 1 lettuce and 1 radicchio wedge on each dinner plate.
Place 1 artichoke bottom, cup side up, beside lettuce on each plate; reserve any extra for other uses. Mound shrimp equally in artichokes on plates, letting shrimp spill over edges. Arrange tomatoes alongside.
Spoon about half the Green Goddess dressing equally over salads. Garnish with onion rings, tarragon sprigs, and breadsticks. Offer remaining dressing and salt and pepper to add to taste.