The Hamptons are not enough for Elon Musk. No doubt seeking to get farther away from the stress of that whole Twitter thing, the world’s richest man this weekend arrived at the most glamorous of the Greek islands, Mykonos, and the Greek press has been having a field day.

While some may have expected Mr. Musk to swoop in via a luxury, solar-powered Tesla submarine prototype, the Greek newspaper Protothema reported that he actually used a Gulfstream jet likely running on good, old-fashioned petroleum. He landed wearing “a macho T-shirt and sunglasses,” the paper said. 

Mr. Musk reportedly does not have a yacht of his own, but may have rented one to poke about the Cycladic island’s numerous secluded coves and bays. 

Mykonos is by no means the most beautiful island to grace the Greek seas, but the summertime atmosphere is unique. Any given day in July or August could be described as feeling like World War III is about to break out or has just ended, with a heady mix of wind, heat, loud music, and unbridled exuberance. Everything you may have read about the ostentation, hedonism, and unapologetic decadence of the place pretty much rings — what would be the right word here? — true. Does that mean travelers should follow in Mr. Musk’s sanctuary-seeking footsteps?

That depends. Traveling to Mykonos in summer is not without some unconventional perils. Have lunch at a trendy beach club like one called Nammos and you risk being drenched by a “champagne shower” — an island custom of dubious charm wherein people splash about bottles of the bubbly for strictly celebratory purposes, with no intention of actually taking a sip. True, the wait staff is trained to hold up beach blankets (embossed with the club logo, of course) to make sure nearby diners keep dry, but at the end of the day it is your dry cleaning bill, not theirs. 

If you’re just about anyone other than Elon Musk, there is also the risk that you could go broke. The absence of Russian oligarchs this summer has not done much, if anything, to reduce the price of traditional Mykonos musts like sumptuous meals at breezy seaside tavernas. Last month, two American tourists on the island were stuck with a bill for about $600 for a plate of crab legs and two drinks. They are suing the restaurant in question, but that episode underscores the reality that Mykonos is by no means an island for penny pinchers. 

Hotel room inventory is going, going, and approaching gone as tourism in Greece rebounds despite a stubborn resurgence of Covid in the country, with Mykonos among the hotspots. A “deluxe double sea room” at the Wild Hotel on a Tuesday or Thursday in July will set you back around $600, and a suite slightly north of $1,000.

Having visited that property a year ago, this reporter can confirm that the price includes a positively sybaritic breakfast, taken al fresco above a private curl of beach. 

The Wild’s sandy cove, incidentally, is right around the corner from the larger beach of Agia Anna, where Mr. Musk was photographed wearing that “macho” khaki T-shirt as he stepped aboard a small boat that may have been spiriting him to a nearby yacht. It is not the best beach on the island, but it will do.

Mykonos has a surprising number of excellent beaches relative to its size, which at 33 square miles is about thrice the area of Fire Island. The sandier and more popular  beaches are all  on the south side. The northern ones tend to be more pebbly and are tough to get to without a car. Yet it’s worth making the effort for beautiful spots like Panormos — which is great for windsurfing — Ftelia, and Agios Sostis. The rocky cove of Fokos is home to an off-radar but well-regarded taverna, and you can swim in the translucent blue water with nary a beachside DJ to be heard, nor a superyacht in sight. 

If money is no object, you can have a spectacular time in Mykonos no matter how crowded the summer sees the place get. It is also possible to do some sun-splashed shopping around the whitewashed alley ways of Chora, the main town, and enjoy the special vibe of a Mykonian  beach club over the course of a day or two even in high season. 

The smart money says wait a little, though. By the middle of September, most of those big boats have disappeared, and having Mykonos to yourself is that rare treat about which you will actually want to tweet home.