Buenos Aires tunes into its Italian influences and does ice cream right. Like alfajores, you can find an ice cream shop on nearly every other corner. The major chains include Freddo, Persicco, Volta, and Victoria, but you will find numerous independent stores, as well. The experience is more or less the same wherever you go, and the ice cream is good everywhere, but when you talk to Argentines you will discover that everyone has his or her preference.
(Mine is Freddo. More specifically, the Dulce de Leche at Freddo.)
At each store you will be faced with a major decision: what flavor? There are always 10-30 flavors to choose from, and each one looks and sounds fantastic. If you're really curious, most places will give you a free taste of one or two before you make your final decision.
Sizes range from a tiny joke of a little cone up to a full kilo. It's kind of expensive -- I usually opt for a cup that costs about AR$25, or just about US$6. I guess it's on par with stores like ColdStone Creamery and Maggie Moo's in the United States.
If you're a budget ice cream eater, go on Mondays -- many of the chains offer specials, like 2x1 kilos or a 1/4 kilo of a certain flavor for maybe 40% off.
If it's busy when you go in, you'll wait your turn in line to tell the cashier what size you want, and you will pay up front. Then you will hand your ticket to the server and tell him what flavor you want. If you're the only person waiting to order, it's a little more relaxed and you can just place your order with the first person who acknowledges you, and pay as the server is dishing it up.
Argentines love their ice cream, and after that first bite, you will, too.