I've been in Argentina last week.
This are my advices:
Mendoza: vist the mountains, the places were they make the wine, give yourself sometime to enjoy the landscapes.
Take confortable clothes! the night life is not so good, so there you can relax, drink a nice wine, listen to some music. 4 or 5 days will be OK.
I've never been neither to Cordoba nor Salta, so i can´t tell.
Buenos Aires: minimum, 7 days. It's one of my favourites cities.
Visit the parks, go to La Boca, San Telmo, Recoleta, Palermo, Puerto Madero, practice some tango in "La Viruta", the night life is really cool, lots of bars and night clubs.
I stayed in a really nice hostel, it's new so it's very cheap. It''s located in San telmo so you will be very close to everything. The name of the hostel is Pax Hostel, look for them on Google (look for "Pax Hostel buenos Aires", so you wont have any trouble). I reccomend it a lot, i enjoyed staying with them.
Buenos Aires is full of cheap places to eat. If you come with dollares, everything will be 3.82 times cheaper. But don't leave Argentina without eating an asado! I had a great one in a place called Spettus, in Puerto Madero.
Anything else you nedd, just let me know!