I dont know how late your kids stay up- but most live music here starts after ten, sometimes much after ten.
I think you could take your kids to CAFF- its pretty mellow, not exactly a "restaurant", though, although I think they serve some snacks.
Orquestra Fernadez Fierro is playing there on the third- they are really fun to watch. Also, depends on your kids, but I think Tonolec would be pretty kid friendly- they are modern folk/indio music, really great. They will be playing there on the 13th and the 19th.
Its in your neighborhood, not too far anyway, down Billinghurst near Cordoba.
Its very authentic- no busloads of tourists, no cheezy Carlos Gardel address signs in Filete for sale.
http://caff.com.ar/programacion
If you are ok with your kids being in a place where "things" are being smoked, you might consider Bomba de Tiempo, too- early, on Monday nights, its outside, there are stairs to nowhere and a huge outdoor/indoor factory for kids to run around in, ping pong tables, a thousand people dancing and having fun, and really great drum based music. Very entertaining. I know my kids would have loved it at most any age, and ignored the pot. Its like a disco amusement park...
http://www.ciudadculturalkonex.org/?page=inicio&subpage=evento&item=31_la_bomba_de_tiempo