OK, let’s play a game. Guess how much a spa treatment at the new Aman in New York costs?

I’m lying on a double bed, in my own private Spa House with flickering fire, vast balcony and both hot and cold plunge pools overlooking 5th Avenue. My arms are tightly swaddled to my body in fluffy towels, like a newborn, and I am being spoon-fed honey (yes, actually spoon-fed) by a spa assistant. Apparently this is to regulate my sugar levels, post extreme heat treatment. It makes me feel utterly and absurdly pampered, like I am being nursed without being ill.

I’m the first journalist to trial the three-day wellness immersion at New York’s long-awaited Jean-Michel Gathy-designed Aman hotel in midtown’s historic Crown building, where a suite (they’re all suites) costs a minimum of $3,200 a night and where non-resident membership of the Aman Club costs $200,000, with dues of $15,000 a year. Although good luck trying to become a member; rumor is that all 600 founder memberships have sold out and there’s a waiting list.

What membership gives you, as well as being front of the queue for Aman’s 34 global properties, is access to the hotel’s club lounge spaces (which include a cigar lounge, wine bar, basement jazz club, an Italian restaurant called Arva and an outstanding Japanese restaurant, Nama). And Aman’s global flagship wellness and medical spa. “Our owner is passionate about wellness,” the director of wellness operations, Shinichi Kiyose, says of Vladislav Doronin, Aman’s Russian-born owner.

The Aman design team has always paid special attention to its pools.

Which is why Doronin has set aside three floors, covering 25,000 sq ft, to cater to the minds, bodies and spirits of the world’s super-rich. The spa, naturally, has all the gear: cryotherapy, an infrared sauna, IV infusion rooms and a 20m pool with double-height ceiling. But Aman NYC has stepped it up further, adding infrared treadmills and all the latest diagnostic equipment – including Brain Gauge Pro, which detects how different stimuli affect cognitive function.

For those overnight hotel guests or Aman Club members who want a wellness deep dive, three personalized immersions are offered: weight management and detoxification; sports performance enhancement; and mindfulness and stress management, which I’m trialing.

As well as an initial consultation and analysis by a traditional Chinese medicine doctor (there are also ayurvedic and naturopathic practitioners), activities include private movement sessions such as yoga and personal training, spa treatments, an IV infusion and CellAir (intermittent hypoxic training, often used by athletes to improve performance). I’m wearing a mask over my nose and mouth that delivers restricted oxygen, mimicking the effects of altitude training – as if I’m atop Mount Kilimanjaro.

It makes me feel utterly and absurdly pampered, like I am being nursed without being ill.

For someone who struggles with mindfulness, the private meditation session was particularly great; in one hour I trialed three types, so I could select which worked best for me. I also had an otherworldly Thai hot-oil massage (ask for Pauline, who got rid of my headache with her wizardy fingers) and an appointment with the impressive Harvard-trained physician and medical chef Dr. Robert Graham, who practices integrative medicine.

Let’s go back to the Spa House, where I lay blissed out by my first ever banya. If you’ve never had this particular Slavic healing ritual, here’s the drill. I lay on a marble slab in a vast sauna, with iced eucalyptus leaves placed on my face, as Igor, an experienced Ukrainian banya therapist, used bundles of oak leaves to draw the hottest air from the top of the sauna and swoosh it over my body to get a proper toxin-busting shvitz going. He also used the leaves to tap me all over, perking up the lymphatic drainage system, with the occasional thwack, like an enthusiastic conductor, to slough off dead skin. He then popped me in the icy-cold plunge pool, then the hot plunge pool while supporting my head and whooshing me around in the water.

Can we blame the Aman’s prime location on Fifth Avenue for its astronomical prices? Why not!

After all this temperature change, and sensory overload, my body and brain didn’t know my arse from my elbow. For a few euphoric minutes I believed I saw heaven and felt the soft winds of paradise. Then I opened my eyes and realised it was the LED shining overhead and a polluted breeze blowing up from bustling 5th Avenue.

While skirting the pain-pleasure threshold, I asked about Ukraine. Igor told me that his brother and niece are both fighting on the front line and that he desperately wanted to join them, but his mother told him to stay in New York and make money to support the family and the war.

Anyway, you’re waiting for the answer. My three-hour banya, one of the most popular treatments at the new Aman, cost $3,200. And while it was very nice, memorable even, you can get a thwacking with oak branches at Wall Street Bath & Spa for only $60.

If you have deep, deep pockets, though, the Aman’s three-day immersion is excellent. Instead of leaving broken and hungover after a long weekend in New York, you head home perky as a Central Park squirrel, with mindfulness practices and a new respect for oak leaves. I just hope lots of those dollars trickle down to Igor and his family in Ukraine.

Alice B-B is an Editor at Large for Air Mail