It is totally safe to go to Argentina! It is just as safe as America, in fact probably safer in some areas! Theft is definitely not a problem in Buenos Aires (unless your an idiot) and you will be perfectly safe using public transportation. Okay, here are the biggest problems for smart and adventurous tourists in Buenos Aires: road rage - people drive INSANELY in Buenos Aires and not all intersections have traffic lights. Also, you shouldn't hire a taxi off the street unless it has a license in it's window. But, the city is fine besides those few problems.
Here are the three places I would recommend going in Argentina: Buenos Aires, El Calafate and Ushuaia. I haven't been to Igazu Falls, but I hear it's supposed to be awesome!
El Calafate is totally safe as well and has a beautiful glacier, Perito Moreno as others. My only caution there is not to try to go down to Perito Moreno by yourself - get a tour. El Calafate is one of those places where you have to plan ahead.
Unfortunately, when I went to Ushuaia I was sick, so I didn't get to see much. But here's what I know: Ushuaia is famous for being the southernmost city in the world (although the southernmost city in the world really is Puerto Williams, Chile, but Ushuaia is close to that city). At the center of the city, there is a big sign up saying "The Southernmost City in the World" in Spanish. Since Ushuaia used to be a penal colony, it has a museum of the former prison. There is also a supposedly beautiful national park near it (Parque Nacional de Tierra del Fuego) which I didn't see because I was sick.
Anyway, Argentina is a great place to visit. Although I wouldn't recommend driving there (take taxis or subway in Buenos Aires, tour buses in El Calafate and taxis in Ushuaia, then rent a car for a side trip to Parque Nacional), Google Maps now has driving directions in Argentina, so it's now easier than ever to plan an Argentina road trip.
Thanks for reading and I hope you have a fun trip to Argentina - in my opinion, it is one of the unknown travel gems of the world.