Los Glaciares National Park in Patagonia is one of the most spectacular sites in the world and also a UNESCO World Heritage since 1981. Just so that you see the magnitude from the very beginning: when we are talking the glaciers here in Patagonia, we are talking the largest chunks of ice outside Greenland and Antarctica, and we are adding to that the largest lake in Argentina (Lake Argentino) and several other glacier lakes.
Your hub point should be the town of El Calafate and getting here depends on the distance you are traveling. If you have flown south to Ushuaia, you can risk it and take a bus over the 800 km distance to El Calafate. It might be stressfully long (around 20 hours), but it’s cheap and you get to enjoy the scenery and some of the people you meet. If you are not on a budget, the plane is always an option: El Calafate International Airport has daily flights to Buenos Aires, as well as to several other Argentinean cities, including Ushuaia, Trelew and S.C. de Bariloche.