Fleni is the closest hospital (Libertador y Blanco Encalada), can't comment on experience as I've never been. Favaloro is the best hospital I've had 1st hand experience with, though my husband said Aleman was good too, both are a bit of a trip away from you though.
For labs, I'm a fan of Rossi, there's a sede in Belgrano near Cabildo y Blanco Encalada.