Jeffrey S.
Yelp
It's possible that this is the most popular sunrise in the state. Certainly, at some point in your life, you've seen a photo of this arch at sunrise. Some screensaver somewhere, some wallpaper, some background in a PowerPoint--this is a really popular place to pop a pic.
Need more evidence of that? Try coming here in the morning to set up your shot. You won't be alone. In warmer months, and especially on weekends, I've heard it gets darn competitive. You can look up videos and see the tripods all over the place, so if that's what you're after, then come early, try to stay warm, and also, try to keep your cool.
As for me, I've never fought the morning fight but I have been at sunset and at midday. Both are excellent options (though sunrise is very popular for good reason--it faces east and the entire underside will light up on good mornings) especially if you want to avoid crowds. No matter the time of day, though, you're going to be with other people.
We hiked it in February and there were always 6-8 parties at the arch. The hike itself is pretty simple, and though it's longer than I remember each time, it's still very short. Just up and around a large hill, then down to the arch. Climb back up and over, and you're out. It's a big loop and the whole thing won't take you more than 20 minutes, but you'll obviously want to stop and look at the views and spend some time at the arch, so 20 minutes is just walkin' time and not gazin' time.
Be careful out there, stay off the arch, and be courteous to others. I have had plenty of (non-sunrise) shots of the place, as everyone wants to get in on it but has always been good about taking turns.