El Chalten is known as the Trekking Capital in Argentina. It is located 220 kms north of El Calafate, in the riverside of Rio de las Vueltas, within the area of Los Glaciares National Park at the base of Cerro Torre and Cerro Fitz Roy mountains, both popular for trekking and hiking tours. It is a small village with less than 2000 habitants. The closest airport is located in El Calafate. From there you have to catch a bus to El Chalten, which takes around 3 hours.
Patagonia Trekking Tours season in El Chalten goes from october to april. There are lots of trails and campsites along the way, which gives you the oportunity to take your own self-guided trekking expeditions, which most of them will last not longer than one day. You should bring clothes for all type of weather conditions, because you can always get unexpected climate conditions even during summer.
The trail to Lago de los Tres is one of the most popular treks in Chalten, but also one of the the most difficult ones. It is a one day trek with amazing views of Mount Fitz Roy, absolutely worthwhile.
The trek to Loma del Pliegue Tumbado is one of the musts, as you will get a fantastic panoramic view of the village. There are two main viewpoints along the way: Mirador Cóndor (from where you will be able to watch condors flying across Fitz Roy river) and Mirador Águilas. Both viewpoints are easy to get to, and therefore a nice trekking for the family even with young kids.
Another popular trail in El Chalten, is the one that takes to Laguna Torre. It is also a low difficult 4 hours trekking with a distance of 12 kms. There are also some viewpoints along the way before you get to the lake at the end of the trail, where you will be delighted by small parts of glaciers that come from the Grande Glacier.
Finally, I would also recommend the trekking to Laguna Capri, a really easy trail of 6 kms, than can be done within 2 hours. From the Capri lagoon, you will get really nice views of Fitz Roy Mount, perfect spot for nice pictures. There is also a very nice campsite by the lagoon.