Most international flights arrive in the evening. Transfer to your hotel of choice, either Belmond’s sea-view Miraflores Park, set in a glass tower, or the art-rich boutique Hotel B, occupying a Belle Epoque mansion.

Take at least one day in Lima, though more would be rewarding. The city isn’t charming, but it does have a wealth of highly acclaimed restaurants and several impressive museums, such as the MAC Lima, dedicated to Latin American contemporary art, and the Museo Larco, with one of the world’s largest collections of pre-Columbian art. (Read more about dining options in Lima and other cities in this itinerary.)

Fly from Lima to Cusco and transfer by private car about 45 minutes northwest into the Sacred Valley, the heartland of the Inca. Check into one of our three recommended properties there, either the Explora Valle Sagrado, best suited to active travelers who enjoy hiking; Sol y Luna, a colorful property with lush gardens and excellent restaurants; or Belmond Rio Sagrado, a small and generally contemporary hotel that offers a very high standard of service.

After arriving in the late afternoon, settle in and relax, perhaps enjoying a spa treatment before dinner.

Spend at least two days in the northwestern Sacred Valley to explore its incredible wealth of sights. Take one day, for example, to visit the spectacular salt pans of Maras and the experimental agricultural terraces of Moray, having lunch perhaps at nearby Mil. And take another day to visit Ollantaytambo (it’s less crowded in the morning), perhaps Pinkuylluna across the valley and/or Pumamarka a bit farther on. A third day that includes Chinchero, with its artisan craft market and a 17th-century church built atop an Inca palace, would not be wasted. Read more about these lesser-known ancient sites.

Transfer to Cusco via the northerly road, stopping en route to explore the ruins of Pisac, a three-part town set atop a cascade of scenic terraces, and Sacsayhuamán, a religious citadel just outside Cusco that’s famed for its massive stones fit together with exquisite precision.

Check into one of our recommended hotels in the city. Two Belmond properties stand adjacent to one another on tidy Plaza Nazarenas: the Palacio Nazarenas, with 55 suites in a former convent and palace, and the 122-room Hotel Monasterio in a converted monastery. Across the square is Inkaterra La Casona, a delightful 11-room hideaway in a thoughtfully updated mansion.

Dine tonight in your hotel or at one of our recommended restaurants in town.

Make a full-day excursion to Machu Picchu, traveling to and from the iconic ruined city aboard the Belmond Hiram Bingham train. It takes about three and a half hours to travel between Poroy station just outside Cusco and Aguas Calientes at the base of the ruins. When not dining on a multicourse lunch, guests can enjoy live music and (included) drinks in the bar car.

If you wish to spend more time at Machu Picchu in order to see the city at sunrise and/or to hike Huayna Picchu (a sugarloaf mountain overlooking the site), spend the night at Machu Picchu Sanctuary Lodge, the only hotel adjacent to the ruins.

Otherwise, return with the Hiram Bingham to Cusco, having a gourmet dinner on board (and maybe another pisco sour or two in the convivial bar car).

Make an excursion into the less-visited section of the Sacred Valley southeast of Cusco, the Valle del Sur. Start at Tipón, which has a series of terraces notable for their still-functioning Inca water channels and panoramic valley views. Nearby is Pikillaqta, a surprisingly vast Wari city destroyed (but never resettled) by the Inca. Its impressively tall ruins and oddly claustrophobic streets feel haunted to this day. Continue on to Andahuaylillas, a town known for its spectacularly colorful 16th-century church, and perhaps a bit farther to Huaro, which has a similarly elaborate church that has yet to be restored.

Back in Cusco, pay a visit to the Coricancha, a former temple to the sun god and the most important religious site in the Inca Empire. A church now stands atop (and amid) the temple’s original stonework. Climb the bell tower for magnificent views of the city.

This is a rather full day; if time permits, take one day to see the Valle del Sur and a second day to enjoy Cusco.

Fly this morning from Cusco to Arequipa, ideally on the daily nonstop flight (it’s also possible to connect through Lima). Transfer from the airport to the Colca Canyon, avoiding the city center. Skirting around Misti and Chachani volcanoes, you’ll enter a reserve dedicated to the protection of vicuña, a wild relative of the alpaca that can usually be spotted right from the road.

Continue over the Mirador de los Andes pass at an altitude of more than 16,000 feet before descending into the Colca Canyon, a valley transformed into a vast work of landscape art by innumerable agricultural terraces.

The drive from Arequipa to Belmond Las Casitas takes between three and a half to four hours. Check into your room, ideally a spacious Casita With Valley View. (Watch our editor's video of the two hotels Andrew Harper recommends in Arequipa and the Colca Canyon.)

Spend a full day in and around Belmond Las Casitas. I highly recommend starting with the “Breakfast in Tapay” excursion, involving a private chef-prepared breakfast at the scenic Tapay viewpoint, where condors soar on thermals up out of the dramatic canyon. Stop also at the better-known Cruz del Condór viewpoint, and be sure to insist that your driver pauses at the viewpoint overlooking the “Amphitheater,” a particularly scenic section of terraces.

Take the afternoon to explore the ruins of Uyo Uyo, go on a hike or horseback ride, or relax and enjoy the amenities of Las Casitas, including its pool and spa.

Transfer back to Arequipa after breakfast. En route, perhaps make a short detour to the Sumbay Caves, home to petroglyphs dating back more 6,000 years.

In Arequipa, check into CIRQA, a contemporary hotel occupying a historic white-stone building a short walk from the Plaza de Armas, the heart of the historic center (reserve nothing smaller than an Aposento Room).

Room rates often include half-board. Whether yours does or not, dinner in the hotel’s romantic restaurant is certainly a good idea.

Take a half day for a guided walking tour of Arequipa, a beautiful colonial city that rivals Cusco in charm (but draws far fewer tourists). Start perhaps with the ornate church of La Compañía, noted for its brightly painted San Ignacio Chapel and rather Moorish-looking cloisters, now home to cafés and boutiques. Stroll through the San Camilo Market, still geared toward local shoppers, with gaudy stacks of produce and various other wares for sale. Finish in the sprawling Santa Catalina Monastery, a functioning colonial-era convent painted in saturated orange and sky-blue tones, now open to visitors. It’s surely only a matter of time before the Instagram hordes discover how photogenic it is at every turn.

Take the rest of the afternoon to shop and explore on your own, and/or relax at CIRQA.

We had a tasty Italian-Peruvian fusion dinner at fashionable Mumis, but Arequipa has no shortage of fine restaurants should you be in the mood for something else.

Transfer back to the Arequipa airport this afternoon and take a flight to Lima. Change planes and return to the United States, likely arriving early the following morning.