Prepare salad first so flavors have time to combine: Halve the cherry tomatoes, dice cucumber and slice onion. Place in a medium bowl with remaining salad ingredients; toss to coat evenly. Cover and refrigerate.
Heat a large skillet (or indoor/outdoor grill). Mix turkey with salt and pepper and shape into 6 patties. Cook or grill thoroughly until no longer pink in the center.
Thinly slice avocado and tomato. Place burgers on buns and top with tomato and avocado slices. Serve with salad on the side. (Serving size: 1 burger with bun, 3/4 cup salad)