• -49.2791-72.98814 Laguna de los Tres. 8 hr (mostly easy) round trip from the town. There are outstanding views of the Mount Fitz Roy range along the way. The trail ends at the cobalt-blue Laguna de los Tres, at the base of Mount Fitz Roy. The last 1.5 km of this hike are very steep and exposed, and as a result some hikers choose to overnight at the nearby Campamento Poincenot prior to climbing the difficult last stretch, though its quite possible to do the whole trek from town. A 500 m well marked additional trail winds around to the left of Laguna de los Tres and leads to a spectacular, cliffside overview of Laguna Sucia, some 200 m below Laguna de los Tres. 

• -49.325-73.00085 Laguna Torre. 6 hr easy round trip that leads to a lake at the base of the dramatic Cerro Torre, which, although only 3,100 m tall, was not summited until 1975, a generation after all the 8,000-m+ Himalayan peaks had been conquered. Cerro Torre's near vertical walls and a permanent, unstable ice veneer at its summit defeated all earlier attempts. 

• A 24-km round trip hike (about 6-7 hr) that takes you above the valleys to see views of both Cerro Torre and Fitzroy to the north, and the Rio Tunel Valley to the south.

It is possible to combine the Laguna de los Tres and Laguna Torre treks using connecting side-trails and available camp sites that create a loop. In addition the following trail can be done:

• Cerro Torres, Mt. Fitz Roy, Laguna Marconi & Laguna Diablo Round Trail. Distance: 92 km. Altitude range: 783 m. Total climb: 2,582 m. Total descent: 2,605 m. Duration: 3-5 days. Grade: Medium to easy. Recommended: warm, weatherproof clothes, and hiking boots.
  This is a beautiful trail that combines most easy to reach sights of the El Chalten region in a long trail with 3-5 overnight stays. No registration with the park office is needed for this trail. There are many camping options along the way (see OpenStreetMap), so it is not necessary to stick to the three-night option explained in the following. Furthermore, Mount Fitz Roy can be done in the evening or the morning, depending on the weather and expected clouds.
  The 3-night trek is recommended as follows: (1st day) El Chalten to Laguna Torre and from there to the camp ground of Mount Fitz Roy. See the sunset or sunrise at Lago de los Tres. (2nd day) From Mount Fitz Roy camp ground hike down Rio Blanco on its western side to Laguna Piedras Blancas with the beautiful glacier, from there further through the picturesque forest by Lago Eléctrico to the far end of the trail at Laguna del Marconi. Here, depending on your time and considered camping options, you might go further to its glacier to the west or the impressing Laguna Loe, its waterfall and its glacier to the north. At the end of the day, hike back until Ruta 23, where right before it you will find a camp ground. (3rd day) Hike into the privately owned Huemul Reserve up to the wonderful blue Laguna Azul and from there by Laguna Verde up to Laguna El Diablo, which is the farthest point of the trail from El Chalten. At the second half of the day, hike back from here directly to Ruta 23, and up Rio Blanco again, but on its eastern side this time until the Laguna Capri camp ground. (4th day) An easy hike down to El Chalten in the morning.
  Download coordinates (click Export).  

The -49.4364-73.19371 Viedma Glacier is the reason why most experienced trekking tourists come to El Chaltén. However, meant by "experienced": 1) reasonable fit, 2) well-considering the weather, and 3) having the right equipment for registration (free) with the park office (especially harness). Inform yourself before heading to El Chaltén what is needed for the (latter) registration and bring everything with you—getting and renting things on site is more expensive and can be a hassle.

• -49.3939-72.868956 Viedma Glacier Boat Tour (start from Bahia Tunel, reachable by car). This is the easy way, referred by most packaged tour tourists, but you will not see much of the glacier, only its end. A boat trip combined with a glacier trek on the Lago Viedma and the adjacent Glacier Viedma. No longer possible due to the receding glacier as of November 2023. 

• Viedma Glacier Round Trail (blue) (Huemul Circuit). Distance: 63.6 km. Altitude range: 1,161 m. Total climb: 2,593 m. Total descent: 2,592 m. Duration: 3-4 days. Grade: Medium to difficult. Recommended: warm, weatherproof clothes, hiking boots and harness for river crossing.
  Also called Huemul Circuit Trail, this is a very exciting, but potentially strenuous trail, for which many experienced hikers come here. The harness can be rented for ~US$6–7 per day in town, and one harness is often sufficient per group. In addition, the registration requires that you show a cooker and gas container, although you may be able to hire one. For all additionally necessary information, refer to the park office.
  Download coordinates: GPX, KML.  

• Viedma Glacier Lower End Trail. Distance: 55.5 km. Altitude range: 812 m. Total climb: 2,183 m. Total descent: 2,180 m. Duration: 2-3 days. Grade: Medium to difficult. Recommended: warm, weatherproof clothes, and hiking boots.
  Registration is not required for this trail, but the trail should not be undertaken when the round trail is not recommended due to the bad weather. A harness could be rented, but there are many people along the trail, which will help you with their harnesses over the lower part of the Tunel River. Otherwise, you can just cross the river (with wet feet) a little downstream were it divides.
  You can do the trail in two days, either hiking up to Paso Huemul in the evening or morning. The trail between El Chalten and the camp site is 6-8 hr. Hence, it might be better to: 1) hike in the first day until the camp site, and see the sunset onto the glacier from there in the evening, 2) spend the next day hiking up and beyond Paso Huemul and exploring the region around the view points and even down until the end of the glacier, and hike back to the camp ground in the late afternoon, and 3) on the third day hike back to El Chalten.
  Note, on the way from El Chalten, you have to go down a hill right before the Tunel boat station. This hill should be descended inside the farm land towards the mountain, otherwise you will have to fight with plants full of spikes.
  Download coordinates (click Export).  

A dead-end ripio road (about 37 km one way) leads you to the very remote Lago del Desierto through a wonderful valley along a river. You can do easy hikes and strolls there and enjoy the peace and quiet.

Besides the easy trails there do seem to exist considerable further even demanding hiking trail, which however are not available on OpenStreetMap. So, you need to consult another source if interested. It is even supposed to be possible to cross into Chile to Villa O’Higgins from here (2-3 days). (In case you find additional information, put them here to help others.)