I have to say, this is one of my favorite places on earth. There is something incredibly special about Arches National Park. Even though I live in Cincinnati and am a mother to 4 boys, I've managed to get to Arches 4 times since 2007 when I first visited. I love that it is compact but there is so much to see and do. I love that in one day, you can see so many amazing sites.
My advice to anyone visiting for only one day: get there early and go straight to the Delicate Arch parking lot and hike up to this unbelievable arch. Once you arrive, spend time up there! Don't just get there, take a few pictures, and go on to the next spot. Sit down, have a snack, explore all of the different angles of the arch. Take some fun photos underneath the arch (ours usually involved some sort of crazy jumping photos, or even a handstand). Take in the beauty as long as it takes (at least an hour). When you've gotten your fill, work your way back down to your car and go back out to the main road and go right to where the hike for Landscape Arch is. Landscape is another special arch. Enjoy it and if you have time, explore that area. Once back at your car, work your way to the Windows section. Climb all around them and visit Turret Arch while you are there. See the Windows from there. Don't miss a quick visit to Double Arch on the other side of the parking lot. It is a cool one. Lastly, stop by Balanced Rock. Don't just view it from afar but park in the lot and walk around the entire rock. It is spectacular.
There is so much more to Arches but if you only have one day, that is what I'd do. It is a special park and a "don't you dare miss" spot if you are anywhere near Moab.