Boil potatoes on medium for 40 minutes, until tender when poked. When eggs are boiled, drain boiling water off, then cover with cold water. Leave eggs in pan with cold water, and tap each one against side of pan to crack shells. When completely cool, drain water from eggs and peel. (HINT: Cracking them in water makes peeling a snap.) Drain water from potatoes and allow to cool to room temperature.
Dice potatoes--peel only if you want to, as they taste great with peels left on--and peeled eggs into a big mixing bowl. Lightly stir in onions, celery, and vinegar. Add salt and pepper and mayo, and lightly toss to coat. Garnish as desired. Chill, covered, for 2 hours. Serves 8.