Swarovski Crystal Worlds, Austria: The world's most dazzling attraction

You could wrack your brains for many hours over the question of what a giant jellyfish, several skulls, a 1963 Shirley Bassey dress, Lenin's tomb and some old bits of curtain from the Academy Awards have in common. Of course, once you've been through Swarovski Crystal Worlds in the steps of 12 million other visitors, it all becomes obvious – at least in some respects. It also remains confusing, although that's contemporary art and marketing for you. My point is this, however: a wander through Swarovski Crystal Worlds makes you feel as if you've blundered into some enchanted kingdom that might also be from another dimension. It's weird and wonderful, bringing together the most unexpected things, only half of which you'll understand. But isn't that what any travel is all about?

Let me say something at the outset: I'm the most uninterested shopper in the world, and when it comes to home décor prefer a sort of monastic minimalism. I've never bought anything from Swarovski, and the thought that people might want to clutter their shelves with crystal animals leaves me bemused. Not that I'm entirely unaware of the Austrian crystal company: after all, their glittering stores have popped up on every street corner – and in every airport – over the last decade. But of all the things that impress me about Swarovski Crystal Worlds, the greatest is that you don't see the word Swarovski, or any hint of its swan logo, throughout the entire exhibit. Well, not until you come to the giant shop just before the exit.

The whole thing is, of course, a marketing exercise, but a subtle and rather enjoyable one. There isn't a necklace, Stardust bracelet or crystal horse in sight, though there is one single crystal creature. It's the first animal figurine created by the company in 1976, a mouse made from old chandelier components at a time when Swarovski realised (rather belatedly, one would think, even in Austria) that the bottom had fallen out of the chandelier market. It's part of the only straightforward, museum-type display at Crystal Worlds that briefly details the company's history. It arrives right at the end of the visit, almost as an afterthought, but is interesting and has a rather fun cabinet of crystal-encrusted fashion: an Elton John crown trimmed with fur, a crystal-and-copper corset by Vivienne Westwood, some super-model bras, and that dress for which Shirley Bassey must have lifted weights for a month to support.

The visit starts, though, at the gaping mouth of a troll-like creature from which a waterfall gushes. The entrance is tucked under his beard and leads me under a grassy hillside in the first hint that this isn't just your regular corporate exhibition space. Wide-eyed, I traipse down a corridor encased in gold leaf and into a dark, deep-blue space gleaming with spot-lit crystals. At its centre is the world's biggest crystal, hand cut with 100 flawless facets, and the equivalent of 300,000 carats in diamond terms. Beside it, under a magnifying glass, is the smallest crystal Swarovski can produce: 17 facets and just 0.7mm across.

This first room makes a bold statement that nothing in Crystal Worlds will be ordinary. There's also a wall loaded with 12 tons of crystals that seem silver and black until you get closer, and see sparkles of blue, orange and aquamarine. Opposite hangs a screen-print scattered with diamond dust by Andy Warhol, and a glittering melting clock from Salvador Dali.

The next few rooms have installations by contemporary artists that make Salvador Dali seem sedately mainstream, however. 'Mechanical Theatre' by UK-artist Jim Whiting professes to explore the 'dark interface of humans and machines' and consists of a spinning dining table, sparkling clothes on a washing line, and a mannequin whose limbs fly off and dance around the room. Further on, 'Silent Light' by Dutch industrial designer Tord Boontje – one of Crystal Worlds' newest exhibits – features an ice-encrusted tree in a black-and-white room where snowflakes of light drift down the walls. Further on, 'La Primadonna Assoluta' is pared down to a simple crystal dome in which a video of soprano Jessye Norman features soaring opera music.

Some of the rooms are baffling, and seem to require long signboards explaining their deep artistic meanings. I find some of the simplest installations work the best. 'Crystal Dome' is modelled on the geodesic domes invented in the 1920s. It echoes and shifts light, making me feel as if I've fallen down a kaleidoscope. Painted skulls and masks are embedded in the walls, and I'm reflected endlessly in 595 blue mirrors.