If i ever had to move to the capital i would choose:
Parque Chas: It`s pretty much like Buenos Aires in the 50`s... actually... it didn`t change a bit apparently. No huge big annoying buildings, quiet neighbourhood. The bad thing about it is that the transportation seems so so and at night is dark so that makes it kinda insecure.
Flores: It`s not la creme de la creme but c´mon! it`s Flores! =D. More city like than Parque Chas and you have to be careful with "el Bajo Flores" (there`s a huge villa there or something like that). But the transportation is good, the prices not too bad, philosophy school is around, and if you ever read the book "Crónicas del ángel gris" by Alejandro Dolina, you cannot but fall in love with Flores!
Boedo: Another barrio porteño, everything screams tango and Centennial park is pretty close. Transportation: so so. Security: no idea.
Saavedra: seems more secure and nice than the others i mentioned but dull.
Parque Chacabuco - Paternal: i heard they`re ok, check `em out.