Apart from the famous milongas, I want to discover the true tango shows...
A popular and original place I experienced is "La Catedral Club". It's an old cathedral converted to an artistic milonga. People go there to take tango lesson (for 10 pesos) until midnight, and then everybody can dance, but you can also enter without taking lesson, and drink something looking at people dancing (you have to pay a fee entrance, but almost nothing). It's very nice and full of popular argentinian clichés =)