Hiking the spectacular Laguna de los Tres Trail in El Chalten, Argentina is a breathtaking experience (in both senses of the word). It's a ~20km roundtrip trail that leads you to a lonely blue lake at the base of three giant peaks -- Mt. St. Exupery, Mt. Poincenot and the most famous of them all -- Mt. Fitzroy (aka Cerro Fitzroy or Cerro Chalten). The trail is no problem at all if you're in decent shape; the only section that literally leaves you breathless is the last mile or so, where you gain ~1,300 ft in elevation. I would recommend bringing hiking poles.
The weather in Patagonia is extremely windy and mercurial, so plan on staying in El Chalten for at least a few days in order to increase your chances of seeing Mt. Fitzroy. I stayed 4.5 days, which allowed me to hike this trail twice; I couldn't see anything on the first hike because the peaks were totally obscured by clouds.
Definitely do this hike. It is so beautiful that it hurts to leave. You can also read about my full experience & see more pictures at: http://bit.ly/1Brm8Ey