Ecuador boasts many day hikes within a day's radius of Quito. One of my favorites was the Quilotoa Loop, which goes from the emerald green Lake Quilotoa, through the Rio Toachi Canyon, to the town Chugchilán. I stayed at the eco-tourist Black Sheep Inn(complete with composting toilets overlooking the canyon below), and they arranged for a local farmer to guide me on the day hike-- though at his quick-footed pace, we did it in a half-day.
I also loved the eco-lodge Bellavista Cloud Forest, which has a bunch of easy-to-moderate trails leaving from their front door. They also supply butterflies, bird watching, horseback riding.
The most challenging hike I did was to the base camp at Cotopaxi Volcano, the highest active volcano in the world, reaching a height of 19,347 feet (5,897 meters). It rises from a highland plain of about 12,500 feet (3,800 metres), and we hiked-- no special gear needed-- to the base of the glacier at 16,400 feet (about 5,000 meters). They have a small lodge at the base which serves light food and hot drinks.