Your First Trip to Buenos Aires
I first visited in 2004 and have been 6 times since, each time for just a short stay as I am an inveterate traveller and can't bear to go to one part of the world without exploring.
BA has changed in many ways since that first trip just at the end of the awful financial crises that gave the city a rawness that I hadn't experienced since backpacking through Greece in the early 1970s. Though it seems to be good at financial crises, it has much improved.
It was so exciting to hear the music played by the local musicians, for me it was almost more exciting than watching the dancers, as I was a still a beginner tanguera in those days. We enjoyed some very famous orchestras that still play today - among them Color Tango and El Arranque; we danced tentatively at milongas, went to tango shows, attended workshops and met famous dancers - and it was all part of a tango tour organised as part of a Festival.
Unless you are speak Spanish, are a native, or have months to spare I believe that going with a group is the best way to go when you first travel to Buenos Aires - or if you are only going for a short time, want to maximise your visit and don't have time to, or want to plan it carefully.
The Tango Conca Tour is led by 2 of Sydney's most popular and well-established teachers, Fabian and Karina, who are also natives of Buenos Aires. You will find a PDF with much more information on the page - Tango Tour to Argentina 2014.
Check it out - I recommend it!