Pilar, Open Door and Canuelas are the hotspots for polo. Do you have access to a car? There are plenty of places to learn. Polo is not particularly popular amongst Argentine women (that I've seen) but plenty of women play it around the world. And of course, it goes without saying that Argentina is the best place to learn in the world as the best polo in the world is played here.
ETA - Cost-effective and polo are not two words you will use in the same sentence

Not that it's a snobby sport but in general, anything involving horses tends to be the antithesis of cost-effective. Once I got into horses, they were the ones getting new shoes every 6 weeks, not me!