Titilaka is an astonishing boutique hotel standing on the south-western shores of Lake Titicaca, cutting a crisp silhouette of sharp corners, with stark colours and daunting brick walls. But slip inside and everything bursts into life, with the bright stripes of hand-woven textiles, shabby-chic colonial antiques and roaring fires. All 18 rooms have big-sky views of the lake and snowy peaks beyond. Kayaking, mountain-biking and hiking are on offer, but best of all is a visit to timeless Taquile island, where residents still rely on farming and weaving. After a brisk day out, the hotel is extremely welcoming (there are even gulps of oxygen for anyone needing a boost). Meals are home-grown: quinoa chowder, alpaca brochettes and native-potato croquettes stuffed with Andean cheese. Massage room.