Skyline Arch is often overlooked heading to Devil's Garden. You will see a small pull out on the side where you can even capture a photo of the arch from the road.
LOCALS TIP - Access the arch from the back from the Devil's Garden campground. You likely won't see very many people and its a great place for kids to roam and play.
You can park in two places:
38.771994, -109.590922 (main TH access along Arches National Park Road that allows you to hike 0.4 miles RT and <50 feet gain)
38.776650, -109.589318 (Devil's Garden Campground Road Parking) and head to the amphitheater. Continue walking back and Skyline will be directly behind you. My favorite view is from HERE: 38.775224, -109.589788