What time of year are you planning to go? If in the summer you should also consider chilling out on the beaches in Uruguay. Punta del Este is the famous resort (where you can be trendy or laid back as you wish). Alternatively you can go somewhere quieter like Jose Ignacio where you get a very ecotourist lifestyle but with excellent 5* quality places to stay.
Punta del Este is only about 40 mins from Buenos Aires by plane.