Few countries pack as much altitude change into so short a distance as Ecuador, where a single ten-day loop can take you from cloud forest to active volcano to rainforest canopy.
Quito's old town is one of the best preserved in Latin America and worth two full days before you head out — the TelefériQo cable car up Pichincha's slopes gives a proper sense of the city's altitude and the ring of volcanoes around it. A day trip north to the Otavalo market, one of the continent's largest indigenous textile markets, is worth an early start; the best selection and the least crowding come before nine.
South of Quito, the Quilotoa loop threads through Andean farming villages to a volcanic crater lake so turquoise it looks retouched. Hike down to the water's edge and hire a mule for the climb back up if your legs protest — nobody will judge you, and the views on the rim walk either side are reward enough for the effort.
Finish with three or four days in the Amazon basin, reached by a short flight to Coca and a river journey into the Cuyabeno or Yasuní reserves. Lodges here run on generator power for a few hours a day and the nights are properly dark; go out on a night paddle with a guide and a spotlight and you'll likely see caiman eyes glowing red along the bank, plus more frogs and insects than you knew existed. It's a hard contrast with the cool mountain air of Quito, so pack for both extremes rather than picking one.