Where in Argentina should I go for a few days?

I am going to Argentina for 10 day. I know this is way too short, but I have to go back for studies in Chile. I have a flightticket to and from Buenos aires, but I want to see another place as well. I am going to spend new years in Buenos Aires, so I am looking to do something else from the 23th till 26th maybe (dates are flexible).

What place do you guys think I absolutely have to visit? I am ofcourse aware this will probably require flight tickets which is fine. My budget for the flight tickets is approximately 150 euros.

I love hiking, but am also down for cities. Down for whatever actually hahaha. Would love to meet other travelers. Planning on staying in hostels. What do you guys recommend?