Just a few blocks down the street from me is Parque Lezama. During the week I often wander down there for a stroll or to sit on a bench under the shade and admire the Russian Orthodox Church across the street, though I do think that there is just a little too much cyan on the domes of that church. One can usually find men playing chess at one of the tables nearby.
On weekends Parque Lezama gets full of families. On Sundays in Parque Lezama I have heard some fairly good local rock bands performing. They just setup their equipment on the grass and play. Mostly, though, I try to avoid Parque Lezama on the weekends because of the crowd and the vendors selling not crafts but socks, underwear, and other things. More sellers have emerged onto Parque Lezama in the past year. The booths now line almost all the streets surrounding the park. I’m not really complaining, though some people in the neighborhood have done so. I’m able to enjoy the park on other days and there are always plenty of things to do in Buenos Aires on the weekend that I have no difficulty finding an alternative.
If you haven’t visited Parque Lezama on a weekday afternoon then it’s certainly worth the visit. It actually has the potential to be one of the nicest parks in the city if the city would do a little more maintenance of it. There are some really wonderful trees and the historical museum nearby.
Sure, La Boca is to the south and that scares some people. But wander around the side streets to the west of the park, such as Caseros or Uspallata, and you’ll find a nice, little neighborhood.