If you have a week in Quito, Ecuador try summiting the world's highest active volcano, Cotopaxi, in Ecuador.
Cotopaxi is a mythical mountain which sits high in the Andes at 19,300 ft. above sea level. To the Incas it was a storied volcano and it held a respected place in their lore. The Incas gave it the name in Quichua of "Cutu" meaning "Neck" and "Pachi" meaning "Broken". If you look, it does appear like a poncho with no head coming out of it.
Every year, many people attempt to climb this storied volcano. Due to sporadic weather fronts and unstable glaciers, Cotopaxi is not easily conquered. Before attempting to summit Cotopaxi, it is recommended to do training hikes and altitude acclimation for a week or two leading up to the trek. Guides can be found in Quito, and make sure they supply you with all the necessary equipment. Ask around for a reputable company, any of which can be found in La Marescal, in Quito.
The climb starts at midnight and lasts six hours to the peak. Once there you can enjoy the breathtaking views and heaven-like landscape. But only for a short time as once the sun's rays hit the glacier, it can become shaky. Climb well and always pay your respects to Cotopaxi.