On 24 July, 1911, Hiram Bingham III, a young history lecturer from Yale University, climbed a steep slope in the Peruvian Andes and, to his surprise, encountered the greatest archaeological find of the 20th Century: Machu Picchu.

More than a million people are expected to visit the site this anniversary year. Most of them will be day trippers who travel to Peru from the far reaches of the globe, who sit on three-and-a-half-hour train rides from Cusco and spend only a few hours at one of the world’s most spectacular ancient sites before starting their journeys home.

Machu Picchu is relatively compact, so it is possible to see the greatest hits of the Incas in a half a day: the elegant Sun Temple, the surreal Royal Mausoleum, the monolithic shrines of the Sacred Plaza and the mysteriously carved Intihuatana stone. But travellers who are willing to make a multi-day hike along the Inca Trail to arrive at dawn or add an extra day to their itineraries by spending a night in Aguas Calientes, the charmingly tacky tourist town that sits 2,000ft below the ruins, have enough time to explore some of the other wonders lurking in the hidden corners of the Lost City of the Incas.

While the day trippers are coming in by train and the most popular spots of Machu Picchu are deluged at rush hour (roughly 11 am to 3 pm), here are five remarkable but often overlooked sights that reward the most intrepid travellers.

Temple of the Moon

Early birds begin lining up before dawn in Aguas Calientes to catch the first buses up to Machu Picchu, and for a good reason. Only the first 400 people to sign in at the park’s entry gate are granted permission to climb Mt Huayna Picchu, the 679ft high green spike that appears in the background of most classic Machu Picchu photos. While the view from Huayna Picchu is impressive, few of those who climb the peak take advantage of their opportunity to see the even more impressive Templo de la Luna, or Temple of the Moon. Tucked into a complex of caves hidden from the main ruins is an otherworldly shrine — possibly a burial site — built directly into the mountain rock. The Temple of the Moon features some of the finest stonework in Machu Picchu: classic trapezoidal Inca niches and double-jamb doorways.

Mt Machu Picchu

The Machu Picchu citadel is bookended by two apus, or sacred peaks. Mt Huayna Picchu marks the north end of the site; to the south stands Mt Machu Picchu. Both offer spectacular views, but while Mt Huayna Picchu turns away would-be visitors, the summit of Mt Machu Picchu nearly always stands empty.

The reason may be the difference in height. At 1,640ft, Mt Machu Picchu is more than twice as tall as its sister peak. But the reward for the 90-minute climb up flights of ancient stone stairs is the most incredible view that can be achieved (short of a helicopter) of how Machu Picchu was carefully integrated into its natural surroundings. Distant, skyscraping Andean peaks tower in the distance while the winding Urubamba River nearly wraps itself around the main site like a python.

Intimachay

Almost from the moment Hiram Bingham stumbled, slackjawed, upon the main ruins of Machu Picchu 100 years ago, experts have struggled to figure out why the Incas chose such an uninviting — if gorgeous — setting to build in. Much recent scholarship has focused on how the buildings at Machu Picchu were designed specifically to interact with the sun, stars and surrounding landscape. The most famous example is the Sun Temple, or Torreon, where each year on the winter solstice (21 June in the southern hemisphere) a beam of light shines through a window, forming a mysterious rectangle atop a slab of granite.

Equally impressive, if much less famous, is Intimachay. The name, a modern coinage, means “cave of the sun”. This cavern, situated just below the main ruins in a spot rarely visited by tourists, was fitted with a handsome eastern-facing wall containing a single window. For 49 weeks of the year, no light enters the cave’s deepest recesses. At sunrise during the 10 days before and after the summer solstice in December, however, the sun’s first rays briefly shine through the window and illuminate Intimachay’s rear wall. The purpose of this Raiders of the Lost Ark-esque light show is still unknown.

Sun Gate

The Intipunku, or Gate of the Sun, is usually associated with hiking the Inca Trail. Virtually every package tour climaxes with a dramatic dawn arrival at this entrance, timed to witness the sunrise. What few outfitters mention is that Machu Picchu is usually misty at that hour, so the views are often anticlimactic.

You are better off visiting Intipunku during midday, when the crowds from Cusco are elbowing their way up the staircase to the Intihuatana stone. The 60- to 90-minute uphill walk runs from the centre of the ruins along a stone path that is actually the tail end of the fabled Inca Trail. The gate, a set of tall stone columns, was once probably a checkpoint for arrivals from Cusco and beyond. The big payoff is the view back toward the main ruins. Sans the mist, it is the best angle for photos of Machu Picchu.

The Rock Quarry

This large space, littered with cut granite chunks of varying sizes, should be impossible to miss. It is located right between the two popular Machu Picchu attractions, the Sacred Plaza and the Temple of the Sun. Yet thousands of visitors pass through each day without pausing.

What at first glance appears to be a jumble of boulders was probably a workshop where expert stonecutters practiced their trade. (One chunk of granite has been carved into almost-finished steps.) Another large stone, known as Serpent Rock, has snakes etched into its top surface. A recent theory proposes that the Inca Trail was a pilgrimage that concluded within the walls of Machu Picchu; if so, the quarry may have had a sacred meaning as a representation of the creation myth, in which the first Incas emerged after an underground journey.

You will not need to mount an expedition like Hiram Bingham’s to appreciate Machu Picchu, but you will probably spend months planning your trip and at least a few weeks’ pay getting there. So take your time and put in a little extra effort toward a memorable exploration of your own.

Mark Adams is the author of the new book Turn Right at Machu Picchu: Rediscovering the Lost City One Step at a Time