The Austrian town is renowned for playing host each year to a Ski World Cup event when the elite exponents of the sport tackle the vertiginous slopes of the legendary Streif race track.
However, I have never strapped on a pair of skis and it was the lure of playing golf in the shadow of the Hahnenkamm mountain, and adjoining the Hohe Tauern National Park, that saw me head for a short stay at the Grand Tirolia Kitzbühel, which was recently acclaimed Luxury Golf Hotel of the Year 2017 by the Luxury Travel Guide awards.
It surprised me, as I suspect it may some of you, that this Tirolean town is visited by golfers as well as skiers, but Golf Eichenheim – designed by American Kyle Phillips, the man who gave us Kingsbarns – has been gathering admirers since its opening in 2000.
At this point your imagination may lead you to envisage a golfing test involving steep uphill, downhill and sidehill lies that would test the balance of a mountain goat.
However, although there is a difference in altitude of 125 yards between its lowest-lying hole, the 16th, and its highest, the third, much of the course is comparatively flat, particularly to those of us used to playing among the hills and dales of Yorkshire.
It demands attention right from the first tee when the player has to be both accurate and long in order to thread (hopefully) his or her second shot between a narrow gap bordered on each side by heavily tree-lined, rocky slopes.
Just two holes on and after playing through the golfing equivalent of the eye of a needle at the first – the reward for which is a first view of the Wild Kaiser mountain - the tee at the par-5 third is like hitting off into space, with a massive drop to the wide fairway below.
It is hard to judge where your ball will finish as it arcs its way to the fairway – or surrounding trees – but it is not critical as the hole is 527 yards off the yellow tees and it will require at least two more shots to reach the green for all but the longest hitters.
However, choosing the right club to use on Golf Eichenheim's five par-3s, at all of which the green sits way below the tee but for at the sixth, is part science, part feel and - at first time of playing – part luck. Anyone who meets the challenge to eye, mental calculation and technique by hitting close to the pin is afforded immense satisfaction.
Because of heavy rain, the greens were not as fast as reputation had it they would be, but their subtle undulations put a heavy emphasis on choosing the correct line. Negotiating water provides an additional test on seven of its holes.
The clubhouse overlooks the course and its glorious mountainous backdrop and was a welcome haven serving, in this writer's view, arguably the best hot chocolate in the world. Here the Golf Bistro has an open display kitchen and you can watch your food being prepared before dining, should you choose, on the terrace overlooking the 18th green.
Adjoining is another of the dining options to be found at the Grand Tirolia Kitzbühel – the Herbarium, which includes a cocktail bar where local flora are used in both alcoholic and non-alcoholic beverages. The Herbarium's cocktails are intended to increase the imbiber's well-being. Improving your golf score the following day is not guaranteed.
No matter, you can always forget your cares – whether the result of a less than satisfactory round of golf or life's day-to-day stresses – at the Grand Alps Spa, one of the most opulent to come to my attention and honoured as the Best Luxury Resort Spa in 2014.
It includes both an indoor and outdoor swimming pool, an oriental Hamam, a Russian Bania and a classic sauna landscape including a Finnish sauna, bio sauna, a Tyrolian herbal bath and two steam baths.
Many of the Grand Tirolia Kitzbühel's 81 rooms and suites provide, unsurprisingly, mountain views and breakfast can be taken on the balcony of your room or in the Eichenheim restaurant, which has a terrace overlooking the golf course.
During my stay three finalists of the Hole In One Million Dollar Challenge, run in conjunction with American Golf, each attempted to win the specified amount at the par-3 second, having qualified by recording an ace at one of the Challenge's 40 associated courses across Portugal, mainland Spain, Majorca and the UK.
The cash remained unclaimed, but all three enjoyed an all-expenses-paid trip to this luxurious Alpine destination where guests can feel like a million dollars – and that's whether they are skiers, golfers or just there to take in the Tirolian air.
Chris Stratford is a member of the International Golf Travel Writers' Association.