I wouldn't say it is a "dangerous" neighborhood overall but you should get a sense of the streets during the day. There was a period when a number of blocks just south of San Juan, maybe around the 2200 / 2300 blocks were a bit hairy, but other than that nothing that bad.
There are a number of old bars along San Juan, and one in particular is Miramar the corner of Sarandí (I believe) that I have great affection for. Further up is Saverio which is, in my humble opinion, one of the best ice cream parlors in the city. It is also the oldest, though the one on San Juan is not the original from 1909 but rather the second one that they opened in the 50s. There is a large population of people from the north around that area so a number of the bars have folk music and dancing "foklore".
Also, one of the reasons there are so many memorial stones for disappeared in the neighborhood is because the neighborhood was very much a work / middle-class union neighborhood and one of the major goals of the dictatorship was union busting, through torture and murder. The most famous person disappeared in the area was the writer / journalist Rodolfo Walsh, and their are plaques in his memory on the corner where he was disappeared: Entre Ríos and San Juan.
On the corner of Matheu and Independencia is a great bar called Hermanos Cao.
A classic confiteria is on the corner of San Juan and Pichincha: La Helvetica.
And don't worry, there is still lots and lots more for you to discover on your own.
Suerte,
Richard