Steam whole unpeeled potatoes until soft when pierced with a fork, about 30 to 40 minutes. Let cool to room temperature and cut into bite-sized cubes. Place in a large bowl and toss gently with tomatoes, onions and celery.
Dressing: In a small bowl, combine mayonnaise, yogurt and 1/4 cup pesto. Pour dressing over potato mixture and toss gently, gently to combine. Refrigerate for half an hour to one hour to chill.