Dinosaur National Monument has plenty of dry canyons (at certain times of the year-there is snow there right now):http://www.summitpost.org/dinosaur-nati ... s/p-183112
So does the Delores River country.
Grand Junction area has plenty of canyons as well, but most aren't slot canyons if that is what you are looking for. There are a few slots in that area, but they are quite short.
Also, don't be fooled into thinking that canyoneering is just rappelling. Many canyons take climbing skills as well.