A visit to the billionaires Bahamian retreat of Harbour Island and the pared-back luxury of £50,000-a-week King's View. Plus, the £18,000-a-night royal suite at the ultra-luxurious Burgenstock Hotel and Alpine Spa on Lake Lucerne, Switzerland, and the £8,500-a-night hotel Le Grand Controle on the grounds of the Palace of Versailles.