Originally Posted by SJOGuy

You say "plane or bus," but South America is a HUGE continent and if you want to cover a lot of territory, you're going to have to fly between places. (Lima to Cusco, your launching point for Machu Picchu, is 20 hours by bus.) If you have two or three weeks, I would limit the trip to just a couple of countries that neighbor each other, say Ecuador and Peru.

Originally Posted by miikkak

Domestic flights are expensive in Peru&Argentina when paying with "real money" as non-resident but cheap in miles. As a result, getting Avios/LANPass for instance through credit card churn is highly recommendable. Lifemiles can be useful in Peru & Skypesos in Argentina.

Lake Titicaca, Amazon & Huaraz (to see more adventurous part of the Andes) could also be interesting destinations in Peru. Given the limited time you have, I would recommend chosing either Peru&Ecuador or Brazil&Argentina. Otherwise you will likely spend too much at airports&buses. Sidetrip to Easter Island (you can fly there also from Lima) or Galapagos doesn't complicate the trip too much if visiting Peru&continental Ecuador.

Brazil requires US citizens have visas and Argentina&Chile paying reciprocity fees when arriving on international flight. Expect to pay ~150 USD per country (=exactly the same amount charged by US consulates for US visa) and note that changes in short-notice are possible especially in Argentina. Other countries like Peru, Ecuador & Colombia don't paying reciprocity fees nor visas.