Before going into describing the teachers, I want to write a bit about the lodging available in Buenos Aires.
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Budget Traveller: For the first three months I stayed in the Alkimista Hostel
( www.alkimistahostel.com ). It cost me about USD10 per night for sharing a six person room.
Halfway through my stay, I felt I needed my own space so I moved to a single room that would cost me USD20 per night. After much haggling and promises of long term stay. The very nice lady boss of the hostel gave my the single room at a monthly rent of USD200.
The tango traveller might save a bunch with a budget hostels such as this. There are cheaper options in the San Telmo area. It could go as low as USD5 for shared rooms. But San Telmo area is generally very rugged, full of tourist and bohemian flair; basically a hotbed for pickpocketers, robbers and other undesirables.
There are loads of hostels in the others neighborhoods (barrios) that are in the more central areas, for example Congresso, Microcentro. The neighbourhoods are cleaner, safer but a little more expensive.
Long Term Traveller: After three months in the hostel, I was forced to move due to the rising prices. It was a blessing in disguise because I found an studio apartment
( www.castilloargentina.com.ar ) which cost USD350 per month near the less shady part of San Telmo. Sharing the apartment Antra, a latvian girl I met from the hostel, made the rent very affordable. I was paying less and having an apartment, complete with TV, internet, all by myself.
So for the travellers that would be in Buenos Aires for a month or more, it makes sense to rent an apartment. My advise is if you do not wish to pay USD400 for an apartment all by yourself, then find someone whom you get along well with and share the apartment together.
Tango Tourists: Most tango tourist who come to Buenos Aires, they want to be immersed fully into the culture. Tango guesthouses offer them just that. It is essentially like a hostel, but instead of backpackers you have fellow tango enthusias from all around the world. Most tango guesthouse have their live in teachers, free dancefloor to practise and customized tango tours to milongas and classes.
Depending on the price you pay, the quality of the tango guesthouses varies too; from a simple room with a spartan bed, to beautifully furnished bedrooms. You can be sure to pay more than a normal hostel, but the cheaper ones cost less than a rented apartment.
Of course, everything comes with a price, but if you are willing to spend, this is really a good option for tango tourist to come and hangout with the exclusive social network of Buenos Aires tangueros. Often the owner of these tango guesthouse are long time dancers themselves, they can fit you right in to the who's who of Buenos Aires milongas.
A good place I would recommend is the place of La Vikinga Helen ( www.hhcultura.com ). She and her partner Miguel Romero are the organizers of Bien Pulenta, one of the trendy saturday night milonga. She also owns a beautiful, cosy guesthouse near the Congresso area.
Another one which I almost stayed in, was Tango Hogar( www.tangohogar.com.ar ). The nice lady offered me USD300 for a really cosy single room if I stayed for three months or more.
Luxury Tourist: For the people who could afford hotels, I guess a quick internet search would list down the hotels available.
Buenos Aires really have some top class hotels near the Centro, Recoleta and Puerto Madero. But hey, if you could afford those places, you are probably doing very well on your own. 
