The Argentine capital is a very beautiful and lively city. In addition, the downtown reminds the Madrid one (architecturally speaking), which will make all madrileños feel at home. There are many events, from plays in theaters to couples dancing tango down the street, and thousands of places to visit. These are some of the coolest: Casa Rosada, Plaza de Mayo (and the obelisk), Florida Avenue, Colón Theater, San Telmo neighborhood, La Boca neighborhood (the cheapest place to stay), Palermo, the National Museum of Fine Arts, the cemetery and Recoleta neighborhood, the Museum of Eva (Evita) Perón, the Botanical Garden, Costanera Sur Ecological Reserve. As a less touristy place, I recommend the ecovillage Velatropa, a few meters from the UBA (University of Buenos Aires).
Also, Buenos Aires enjoys a great location to do some excursions to interesting places in the country (like Rosario or La Plata) and in Uruguay (Colonia Sacramento, Montevideo).