Zion is a little bit more dog friendly than Bryce. There is one trail that you can walk your dog on, and it's actually longer than 800 feet. Zion is interesting because you drive through the park and then you can take a bus into the canyon, there are no cars in the canyon. But there are no dogs on buses so we just hiked along the trail for a while, letting Marshall get a turn in the little river that was running near the campground.
Zion was nice, but I could see how it would be seriously hot in the canyon in the summer. I think fall and spring would be a great time to visit.