I stayed at America del Sur Hostel on my first trip to El Calafate many moons ago but it remains the best. It is very close to downtown and Laguna Nimez and is just steps from the best place in town to eat Patagonian Lamb (a major bonus in my book). It is affordable, social, and has both shared dorms or private rooms. 

There is a restaurant and bar on property but you're also only a 5 minute walk to everything you need in town.