Given the fact that El Calafate is very far from other cities in Argentina, the best option is to fly.
Most services depart from Buenos Aires although, according to the season, there are connections to other areas in Patagonia as well.
If going by car, then the way is first to Rio Gallegos, along Route 3 and afterwards Route Provincial 5.
Distances from El Calafate to:
Bariloche 1449 Km. (via Route 40)
Bahía Blanca 2075 Km.
Buenos Aires 2727 Km.
Córdoba 2732 Km.
Neuquén 1979 Km (via Route 40)
Puerto Madryn 1388 Km.
Ushuaia 863 Km.
Viedma 1785 Km.