There are many kinds of tango shows. It depends on what you're looking for and how much you want to spend.
Tango casas offer a complete show with dancers, singers, live orchestra, and dinner, catering to foreign clientele. (Senor Tango, Piazzolla, Esquina Gardel, Tango Porteno, etc.) Expensive.
Penas de tango have amateur singers with live accompaniment (piano and guitar) where you have dinner. Bar Rojelio has a pena de tango every Tuesday night and the first Friday of the month. Gascon 1460 between Honduras and El Salvador. Very affordable.
Restaurants around the city advertise a tango night with a singer and live music, sometimes with a dance couple. I discovered Bodega Campo on Rodriguez Pena 264 (San Nicolas) last week on Thursday when a female tango singer is accompanied by Norberto Vogel, bandoneonist, for two sets beginning at 10:30pm. Intimate little restaurant with great food and service. (I had ensalada Capresa and Fettuccini con salsa azul. OMG!)
El Juvenil mentioned above was formerly a dance hall Salon Bailable Juvenil until it closed in 2000. It went bankrupt and was sold at auction. It couldn't reopen as a milonga due to the narrow hallway entrance that didn't meet city regulations. It was one of the best places to see real milongueros dancing socially on a Saturday night. And the admission in those days was only $5.
Anyone who wants to see social tango can find it the milongas where those over 60 attend near the Congreso. The admission is 50 pesos plus the price of a drink.