El Chalten/Monte Cerro Fitz Roy
The trails are often full on this symbol of Patagonia, but it's easy to avoid them. Just get up at 3:30 in the morning to catch the sunrise you'll be all alone. (Although the sunrise wasn't impressive that morning, fading almost as soon as it was there.)
Note: yahoo maps (used by flickr) are just terrible compare to Google maps. Try these coordinates (72.987495,-49.274189,0.000000) and switch to terrain to see the frozen lake and the mountain off to the east.
Read about beating the crowds to this spot.