Hey, like he said above, it really depends on what you are looking for. Recoleta is nice, but also very expensive, and its safety is debatable since I know just as many people who have been robbed there as in other more "dangerous" neighborhoods. San Telmo is a fun place with a lot of foreigners, and a more "authentic" experience could be had on the further side of the barrio, closer to La Boca (the anti-Recoleta: a lot safer than you have probably heard). There are a number of other barrios that expats don't normally think about, like Caballito, Saavedra and Belgrano. I like Belgrano because it is quieter like Palermo, a lot cheaper, and you can easily get back into the center of the city. Also, I have heard of a lot of expats moving downtown, but be warned that this area can be very loud (not the kind of loud you want) late at night and early in the morning. Anyways, like i said before it all really depends on your personal taste and style.
Cheers!