Zion National Park and the national forest surrounding the park is the most famous destination for going Canyoneering in the world.
Escalante National Monument, also in Utah is another very popular destination.
Kanab, UT is a popular destination close to Zion without the crowds of Zion National Park.
Moab has incredible arches and slot canyons to explore outside of Arches and Canyonlands National Park
https://www.canyoneeringusa.com/intro/canyon-ratings has ratings for different canyons around the world.