I suggest you stay away from Confiteria La Ideal, sucks.
You will be very close to Escuela Argentina de Tango, it is at Centro Cultural Borges, in the backyard of Galerias Pacifico. Claude Murga teachs there, she was co-star with Mora Godoy in Tanguera.
However, I suggest you look for techniques clases only. The Sunderland Club is one of the best places. Yuyu Hererra is an excellent teacher. Mariel Altobello too. You can find then in FB. Being in Buenos Aires you should learn to walk.
Tango Shoes, avoid Comme il faut, they don´t have leather shoes, it is all plastic.
Lolo Gerard is an excellent place to make them custom. It is in front of Shopping Abasto.
The place you choose is not the worst in the area. But, at night there is a lot of night life if you stay "in the bajo" (Reconquista and 25 de mayo streets). But if you go up to 9 de Julio is ugly. It is downtown, at night there is no people at streets, just homeless and prostitutes.
There are 2 milongas you will be more or less close: Cachirulo at Maipu 444 on Saturday since 7.30 and El Beso on Riobamba and Corrientes. These are 2 of the most "traditional" milongas.
At Cachirulo they have the rules posted on the wall: 1) Here we dance close embrace or you are out; 2) You only invite the lady to dance through cabeceo or you are aout 3) You pick her at her table and you leave her at her table or you are out; 4) You only dance forward or you are out; 5) You don´t do boludeces (adornitos, voleos, planeos, colgadas, volcadas) or you are out.
At Cachirulo, Canning and el Beso you must call in advance for a table.
Cachirulo is at the Beso on thuesdays.
El Beso is more relaxed but the dance floor follow the same rules.
Regarding cabeceo, after you accept you wait until the man is in front of you IN YOUR SEAT, keep eye contact, then you smile and if he confirms you stand up. Otherwise you will misunderstand it and it will be very embarrassing.
Specially at the Beso, only accept a 3er tanda with a milonguero only if you want to have an affaire with him.
At the other side of corrientes you have Porteño y Bailarin. I don´t like the place, but you should know it.
You can take the bus 140 on Cordoba Avenue and it takes you straight to Palermo:
Canning (Monday and fridays); La Viruta (from wednesday to Sunday)(after 1 am its for free, on friday and satuday after 3.30, before that there are only begginers)(do not take clases there); Milonga 10 (Thuesdays and saturdays), Praktica X (Thuesdays) and Villa Malcolm (it sucks, well, I assume you didn´t travel to go to a place just like the only you can find at home).
To go to the Sunderland Club for classes, you go to Retiro Train station and you take the train the Jose Leon Suarez, you will be there in 15 minutes. You go until Drago and from there it is 6 blocks far. Classes starts at 8. There is a train every 15 minutes.
In summer time you should go to la Glorieta (Same train station, you take the one that goes to tigre and until Belgrano C) ON Saturday and Sundays.
Have fun.
Regards