I am not sure about the most part, as I have a fair number of unforgettable travel experiences.
But the best of the most. In more-or-less chronological order.
Crossing the Atlantic from Southampton to Le Havre to Halifax to New York on the RMS Franconia ( 1956 ).
First of several visits to the Atomic Weapons Research Establishment ( AWRE ) in Aldermaston ( UK ).
Spending a week in Erice ( Sicily ), meeting with my Soviet and Communist Chinese counterparts, hosted by the Italian Foreign Minister. A lovely village overlooking the Sea.
First trip to the North Slope of Alaska in mid-winter, spending time in Barrow and visiting several Inupiat villages by chartered plane.
First trip to New Zealand, Australia, and ( especially ) Papua New Guinea. In Port Moresby the PNG government provided armed escorts wherever we went.
First of many visits to Manus Island, PNG.
Visiting Cape Grim in Tasmania for a day. Visiting Nauru for a week. Spending a week in Nuku-a-lofa ( Tonga ). Sending a few hours in the Solomon Islands.
First of many trips to Bruges, one of my favorite places all time.
Visiting Monte Carlo on a day trip from Genoa just before the cruise ( #10 ).
The 26-day Mediterranean and Black Sea solo cruise in 2010. Stopping in Istanbul, Yalta ( Crimea ( Ukraine )), and Odessa.