The 130km Huayhuash Circuit circumnavigates Peru's Cordillera Huayhuash. It is widely considered to be one of the top treks in the world. It includes numerous passes over 15,000' and up to 16,500'.

Here's a nice article about Choquequirao & the planned "improvements" to get more tourists in.
www.theguardian.com/travel/2014/nov/01/peru-choquequirao-inca-ruins-trek

The super-classic, 100+ km Paine Circuit is the premier backpacking route in Torres del Paine National Park, Chile. It traverses some of the most spectacular scenery on Earth. The much shorter "W" is probably done more often as it covers much of the most best scenery of the Circuit plus allows close up views of the amazing towers & spires for which the Park is justly famous.

Note that there seem to have been some new regulations put in place that make it much harder to legally attempt an FKT, as reported by Sunny Stroeer (2/9/2018):