I’ve never met a Rockefeller and my last name is certainly not Carnegie or Vanderbilt, but during my stay at The Point  I was given a taste of what it must be like to be a bold-named guest of one of America’s wealthiest and most hospitable families.

Originally built in the early 1930s as Camp Wonundra—the mountain home of William Avery Rockefeller (John D.’s nephew)—The Point is now an exclusive 11 room Relais & Chateaux retreat where everything including all food, drink and activities is included and nothing is too much to expect, just as the Rockefellers hosted their friends here for years.

Dinner in the soaring dining room in the main lodge, with its twin walk-in fireplaces,...