Box Canyon is a box canyon in Ouray County, Colorado, United States. A mining camp was established in the canyon that helped the city of Ouray establish itself as a permanent community. Box Canyon is home to Box Canyon Falls, a 285 feet waterfall, with quartzite walls that extend almost 100 ft past the falls. Access to the canyon is through a short, 500 feeā¦Box Canyon is a box canyon in Ouray County, Colorado, United States. A mining camp was established in the canyon that helped the city of Ouray establish itself as a permanent community. Box Canyon is home to Box Canyon Falls, a 285 feet waterfall, with quartzite walls that extend almost 100 ft past the falls. Access to the canyon is through a short, 500 feet foot trail to the base of the falls or a steep trail leading to the top of the falls. A fee is required to use the trails to the canyon.