From the Inca Empire to the Peruvian Amazon with the Nazca Lines

Bucharest, Romania's sprawling and magnificently contradictory capital, layers Belle Époque mansions, communist-era boulevards, and a furiously creative twenty-first-century scene into a city that rewards the curious traveler who looks beyond the obvious. Ceaușescu's colossal Palace of the Parliament — the world's heaviest building and a monument to totalitarian hubris — is unmissable; equally essential is the neighborhood of Floreasca, where design studios, natural wine bars, and acclaimed restaurants have made Bucharest one of Europe's most exciting emerging food capitals. Visit April through June for the most pleasant weather. Transylvania, with Bran Castle and the medieval city of Brașov, lies two hours north through dramatic Carpathian scenery.

Budapest, divided by the Danube into the hilly Buda of thermal baths and medieval castle lanes on one bank and the grand Pest of coffee-house culture and Art Nouveau splendor on the other, delivers the most theatrical first impression of any European capital — whether approached by river as the neo-Gothic Parliament materializes from the water or by night from the Citadella's sweep of illuminated panorama below. The city's celebrated thermal bath culture, rooted in Ottoman-era hammams and perfected in palatial Secession-era pools like the Széchenyi, is an experience entirely unlike anything else in Europe. Visit spring and autumn for comfortable temperatures; Vienna is two and a half hours west by train.

Paracas is a desert peninsula on Peru's southern coast where one of the world's most productive marine ecosystems meets a landscape of dramatic aridity, enigmatic geoglyphs, and ancient textile traditions. Must-dos include a boat tour to the wildlife-packed Ballestas Islands, exploring the red sand beach and flamingo bays of the national reserve, and dining on fresh ceviche. Visit year-round in this rain-free climate, with mornings best before the fierce afternoon winds.

Visegrád commands the Danube’s most dramatic bend from a hilltop citadel that once housed the Hungarian Crown Jewels and a Renaissance royal palace rivaling Italian courts. Must-dos include climbing to the Upper Castle for panoramic Danube Bend views, exploring King Matthias’s restored palace and Hercules Fountain, and tasting Hungarian gulyás with Etyek wines. Visit April through October, with autumn foliage adding golden drama to the sweeping river views.

Brasov is a magnificently preserved medieval Saxon city at the foot of the Carpathian Mountains in Transylvania, home to the Gothic Black Church, fortified walls, and proximity to the legendary Bran Castle. Must-dos include exploring the Council Square, tasting sarmale and mici in the old town, and hiking in Piatra Craiului National Park. May through October offers the best weather, with autumn bringing spectacular mountain foliage.