well if you are traveling by plane you will only spend a few hours max to go anywhere in the country.. so dont worry about that...
main places to go in argentina:
Bariloche
You can see the Andes here.. it has one of the best ski resorts in the world and it is same and VERY beautiful.. it is cold in winter though and its high season on july and august but worth it
Mendoza
You can see them from here too and if you like wine this is the place to go
Iguazu
you wont see the andes but the waterfalls are just AMAZING.. this trip can be done in 2 days and a half so you can do this and go travel somewhere else afterwards
Perito Moreno glacier
i havent been there yet but everyone who has says its just amazing and breathtaking.. its one of the worlds wonders (iguazu as well)
Tierra del Fuego
Lowest point on earth!! IT IS FREEZING
those are the main places.. for the andes i do recommend bariloche.. villa langostura which is closed by its also great.. take your camera!
the places im mentioning and way safer than buenos aires! i wouldnt worry =)
enjoy
If you like cold, you will love the Patagonia in winter.
San Carlos de Bariloche, you will love that city, then Ushuaia, the last city in the American continent, those places are awesome!
Southern Argentina is very safe, all cities there are very safe, people there don't lock their houses. But I don't know what you want.
If what you want is to see the Andes, go to Mendoza. You'll find better locations to visit the majestic mountains there. Good luck.
If I were you I would definitely go to Patagonia
I am studying in Buenos Aires, Argentina for July. I will have a 5 day break to travel somewhere. I really want to see the Andes. What is the best place to go? Since I will probably spend 2 out of the 5 days traveling, I would like to make it worthwhile. What are the best buses to take or planes? Is patagonia worth going to in the winter? This process is just overwhelming to me. I also need advice on a safe place to stay. I will be traveling alone.