Now, for all parents — hear what I say: if at all possible, book a hotel room for the night before you arrive so you can go right in and take a three-hour nap. Otherwise, you might find yourself waiting with two exhausted children for several hours for your room to be available, as we did in Scotland.

Because when that nap is over, the fun truly begins.

To see Paulina’s eyes widen as we stepped out of our hotel into Shinjuku, in Tokyo, with its rushing crowds, flashing neon and bird-tweets emitting from the walk signs was to see a child’s world expand exponentially. “Oh my god this is like another planet.”

Same with Dean as we first walked across the Pont des Arts over the Seine in Paris and his brown eyes took in the Pont Neuf, the Ile de la Cite, the towers of Notre Dame and all the rainy-gray and muted brown stone buildings arrayed before us.

***

The key to making plans is not making too many.

Too little structure and we’d end up wandering the same neighborhoods; too much and the trip becomes a forced march. We always book a few restaurants and, in more recent years, as the crowds have increased, a museum or two.

But that’s all. We reserved a specific time at the Rijksmuseum our first day in Amsterdam, and it was a great morning. Enthused, we decided to try for two museums in a row but balked when we saw the long lines at the nearby Van Gogh Museum. So we had a rijsttafel lunch at an Indonesian restaurant we stumbled across. Then we spent some time in a Tesla showroom, for no particular reason.

We don’t have to be together, all of us, every minute. Dean started taking long walks by himself in Japan, especially along the river in the mountain city of Takayama, and Helene and I sneaked out to a jazz bar in Kyoto one evening while the two of them luxuriated in their yukata robes back at our ryokan (Japanese hotel).

In Paris, after the unfortunate first-class throw-up episode, Dean was laid low for a day, so Paulina and I went up to Montmartre to take in the views and have lunch at a cafe on the Place des Abbesses. Two days later, Dean and Paulina went off on their own with a friend of Dean’s from school. We met them for dessert at Berthillon, the famous ice cream parlor on the Ile St. Louis.