Located about 10 miles from the nearest trailhead, Angel Arch is one of the most remote arches in all of Canyonlands. It might be possible to see it on a mararthon 20 mile day hike, but the harsh mid day light would not do the arch justice photographically speaking. Instead plan an overnight camping trip if you wish to get a good photo of this site. Information on backpacking in the Needles may be found at this link.
The best light for this location occurs between the fall and the spring. The desert light is quite harsh in the summer. There is water along Salt Creek on this route. It should however be treated before drinking.