Rather than experience traditional tango in Buenos Aires at a large tourist show, I particularly liked going to smaller venues and walking through the LaBoca neighborhood to see dancing in the streets. I recommend:
La Cumparsita Tango Bar at Chile 302: A small tango bar in San Telmo with music and a small show in the evenings. 4361-6880 for reservations.
I also enjoyed Bar Sur, for its small tango show, located at Estados Unidos 299. The phone is 4362-6086 for reservations. I really liked this place and La Cumparsita for the local flavor and great Tango. There were very few tourists!
Confiteria La Ideal, Suipacha 384: Opened in 1912, this is a bastion of belle époque grandeur. Make sure to head upstairs for the Tango Milonga in the afternoons. Check out the schedule as there are classes and milongas throughtout the week. It is right out of a movie set and a great place to see older tango dancers in action.
Make sure to spend some time in the area of town known as LaBoca. It is a colorful area with shops, galleries and cafes with people doing tango in the streets. It is somewhat touristy but really fun!