Remember that when it's summer in the United States, it's winter in Argentina, and vice versa. Winters (July-September) are chilly, though temperatures never drop below freezing. Summer's muggy heat (December-March) can be taxing at midday but makes for wonderful, warm nights. During these months Argentineans crowd resorts along the Atlantic and in Uruguay. Meanwhile, traffic-free Buenos Aires has a host of city-sponsored concerts and theater that bring people out into the sun and moonlight.
Spring (September–December) and autumn (April–June), with their mild temperatures—and blossoms or changing leaves—are ideal for urban trekking. It's usually warm enough for just a light jacket, and it's right before or after the peak (and expensive) seasons.
The best time for trips to Iguazú Falls is August–October, when temperatures are lower, the falls are fuller, and the spring coloring is at its brightest. Between December and February the heat at the falls can be suffocating.