When to Go
I recommend going in the spring or fall to avoid the summer heat, especially if you have your dog. I went in late October and it was warm, but just perfect honestly. The crowds weren't bad at all either!
Where to Stay
I stayed with my dad at the Hampton Inn and we loved it. The pool and hot tub had a great view of the mountains at sunset and it was the perfect place to explore Zion. My dog had air-conditioning too, so I felt comfortable leaving her in the hotel while we hiked the non dog-friendly trails.
Hiking Trails
So there's only one trail that's dog-friendly in Zion, and that's the pa'rus trail. It's relatively flat and easy, but still offers plenty of beautiful views. Please read the signs while you're there because when we visited the river had "no drinking" signs for dogs; they had a deadly algae at the time. Keep your dog on leash and away from the water while you visit to make sure they are safe from harm.