You are in the right place and at the right time for polo!
As Smirkypants said, the Tortugus Championship is going on now in the Tortugus Country Club. Today (Tuesday) La Dolfina is playing Chapa II at 4:00 PM. You can get tickets at the fields in the Club (exit Km 38.5 Panamericana). The tournament continues this weekend (Saturday and Sunday 4:00 PM) with the final on Saturday October 10. All weather permitting. Not only does it have to be not raining, but also the fields have to be dry to play.
The second leg of the “Triple Crown” is played in the Hurlingham Country Club (Hurlingham exit off the Camino del Buen Ayre) October 13 -31, 2009 (tickets available on the grounds) and the culmination; The Campeonato Argentino Abierto de Polo, is played in Palermo November 14- December 5, 2009. Tickets are not on sale for Palermo yet, should be through Ticketek soon. Seems like most people buy the abono (“season pass”), and many don’t go to the preliminary matches (stadium seems a bit empty) but an entrance to the Final is golden in this town. You can hobnob with the rich and famous.
With the polo field being a bit larger than 9 American football fields, Palermo, with stadium seating of more than 25,000 offers perhaps a better view, but when you stand on the ground (as you would almost anywhere else) by the boards, you get the opportunity to really “feel” the game.
Aside from the aforementioned tournaments, there are more than 250 polo fields just in the area of Pilar, General Rodriguez and neighboring Open Door (NW of the Capital). In an area called Pilar Chico (off ruta 28 between Pilar and General Rodriguez) you can find a concentration of dozens and dozens of fields in clubs including Ellerstina, Centauros, Polo One, La Indiana, Cuatro Vientos, Pilarchico, etc.
This time of the year, there are sure to be practicas Tuesday and Thursday afternoons and tournaments on weekends.