Angie, Hi. Recoleta, Palermo and Belgrano and most areas in Capital Federal are busy mostly because big buses (colectivo) and taxis frequent them and traffic could be quite something during busy commute hours (to and from work). Major streets like Libertador, Santa Fe, Colonel Diaz, L.M. Campos, F. Alcorta can be busy all day long. Not much public transport at night but still...with a baby. If you have sometime to shop around for a house, I am certain you will find one that just suits you and your family.
If you live in the upper floors (way up there) in any building anywhere in the city then noise might not even be an issue. Say on the 24th floor of any building you can not hear anything from the street. There are lots of building like that around the city and more being built each day.
Green grassy lawns and yards are mostly found in the outskirts of the city (Capital Federal). Commute should be considered.
BsAs is fun. There is never a dull moment, really. Good luck.
Ciao, Grazie.