Place potatoes in a saucepan; add water to cover, and bring to a boil. Cover; reduce heat, and simmer for 15 minutes or until tender. Drain and set aside.
Steam mussels, covered, 10 minutes or until shells open; discard any unopened shells.
Trim tough outer leaves from fennel. Dice stalks to equal 1 cup; set aside. Cut fennel bulb in half vertically; discard core. Cut each half crosswise into thin slices to measure 1/2 cup, and set aside. Reserve remaining fennel for another use.
Combine vinegar and the next 6 ingredients (vinegar through garlic) in a large bowl, and stir well. Reserve 1/4 cup dressing; set aside. Add potatoes, mussels, fennel, and tomato wedges to bowl; toss gently to coat. Cover and chill 30 minutes.
Combine reserved 1/4 cup dressing and greens in a bowl; toss well. Divide greens evenly among 4 salad bowls. Arrange one-fourth of mussel mixture and 2 egg quarters over each salad.