I consider travel to Buenos Aires to be as safe as travel to London, Paris or New York. Of course there are areas you should avoid, but you should not categorize BA as being similar in safety concern to other South American cities like Sao Paulo or Rio - which are considerably more dangerous. A good guide book will detail the areas you should avoid.
The current economic problems in Argentina, though flared up, are nothing new - especially to the people who live there. In other words, with little current world economic news, the financial world has again focused on Argentina, but the same problems were there six months and three years ago.
I was there six weeks ago with my five-year-old son. We do not speak Spanish, and we were very comfortable negotiating the city and walking the streets. We even went to a soccer match, although I did arrange tickets and transportation through a hotel as the areas around soccer stadiums can be a little rough.
I hope you enjoy your trip.