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I usually get to this one from the 4th of July Trailhead by Buckingham Campground. It's about a two mile walk to the basin at the bottom of the South Face that's in this picture.
According to Gerry Roach's excellant guide, there are two harder finishes for this route. One, Princess Leia, goes up a narrow ice hose. The Other, Han Solo, goes right, and finishes with a few rock picthes.
R2D2 isn't listed in Gerry Roach's guide, but it's a good beginners route as you can get off it at convienient intervals by traversing onto the hillside at left.
There is also a trail to the top that goes up the hillside in the foreground, and then up the right skyline to the top.
This picture was taken in late Oct, after an unusually warm Fall. I recently (mid June, 2011) climbed South Arapaho again, and took new pictures as it was in excellent condition. Those are available here.