Things to do in Austin, Texas: The US city that's weirdly, a cool place to visit

We've got the address wrong, surely. My three travel companions and I walk into a carpark beneath a bank in downtown Austin, searching for a cocktail bar called Garage.

Obviously, given the name, it has something to do with a carpark, but who in their right might would put a bar down here, under these hideous neon lights and brutalist concrete columns? Just as we're about to call off the search and return to continue walking down Sixth Street (a string of drinking dens and music venues colloquially known as Dirty Sixth), we spot the neon green Garage sign. And we remember that in the Texan capital, it is the duty of each and every inhabitant to do what they can to "Keep Austin Weird", as the city's slogan goes.

Garage, set in the parking garage's old valet ticketing office, is a surprisingly slick space centred around a circular green tiled bar, that serves excellent craft cocktails. It's just the kind of clandestine place that typifies the quirky Texan capital, where reclaimed spaces add unique texture to the city's sipping, shopping and sleeping scenes.

Earlier in the day I go shopping in a place I never thought I would – inside a bus called Minnie, that once housed a mobile vintage boutique called To The Moon. Later, I have a drink in one of the dozens of historic bungalows-turned-bars that line Rainey Street, one of Austin's top party streets, and another in Container Bar set in – you guessed it – a series of stacked shipping containers.

At some point I also have a poke around Native Hostel, which originally housed a brewery, then shops and factories, before becoming what might be the most achingly hip hostel in the US.

That Austinites would find unusual places to put their shops, bars and hotels shouldn't come as a surprise. This is, after all, a city that celebrates the birthday of Eeyore (the depressed donkey from Winnie the Pooh) every April and that counts a Museum of the Weird, with a robust collection of things such as two-headed sheep and mummified people, as a star attraction. So I shouldn't have balked, really, when my travel companions suggest that, after Garage, we go for a drink in a former brothel.

This is how we come to find ourselves, once again, playing hide-and-seek on anarchic Sixth Street, stopping at a dodgy-looking unmarked door set beneath a naked red bulb, which Google tells us is the entrance to a speakeasy called Midnight Cowboy.