The one I went to was privately organized and you reserved a seat on a bus to get there because it was in the province. I haven't heard of any that are weeklly here. That's news to me but sure makes it more accessible.
They do some folk dancing at the Feria de Mataderos, and they have vendors selling asado, but I would not compare that experience at all with the one I had of going to a special Pena center in the country and literally spending all day dancing continuously with others. The big difference is that at a traditional Pena people come EXCLUSIVELY for the folkmusic and dance. There is no competing commercial activity, I.e. a street fair selling goods. People come to dance ONLY, not to shop around and be entertained watching and maybe trying folk dancing. The other nice thing was that people were extremely friendly and you were seated at group tables where you stayed all day (and could reasonably safely) leave your stuff. Bathrooms and air conditioning also helped!
There is also an occasional round of folk dancing at many of the traditional milongas, but again, it is just a a few dances out of many hours and in my opinion, not anywhere near the intense and extremely friendly (and family) atmosphere of the all day penas organized exclusively to dance folklore with maybe one round of tangos thrown in just for a change! There are folklorico groups throughout BsAs so maybe you could simply google it and look for listings of penas organized by the folklorico societies. Than you know you've got the real deal.....have fun!