I will be living in Córdoba, Argentina... The second largest city in the country. So, of course, I want to see the biggest city as well as the capital, Buenos Aires. I believe a weekend trip is long enough to really get a taste of the grand city without spending too much money.

The best way to get to Buenos Aires seems to be by bus from Cordoba, since the train system in Argentina is said to be rundown and unreliable - something I will definitely avoid.

I can use these websites to book a bus ticket once I'm in the country:

http://www.omnilineas.com/argentina/bus/villa-general-belgrano/retiro/

http://www.plataforma10.com/ar/

This will get me to Buenos Aires and back for around $60 or $70 USD. That's pretty cheap and helps me not exceed my budget.
I can stay in one of these hostels once I arrive:
BA Stop, Buenos Aires Hostel $24/night
Garden House Hostel $30/night
Che Lagarto Buenos Aires $40/night

Tentative Itinerary:
Thursday:
arrive and settle in on Thursday midday/evening
meander around Palermo Soho, which is the largest barrio, and explore the shops and cafes
eat dinner in Palermo Soho at one of the many restaurants
Friday: 
Visit the Bellas Artes National Museum and admire the art and culture honored and exhibited in the museum
Siesta: take a nap!
Visit the Recoleta cemetery...where many famous people are buried... including Evita! I would like to see where she lies (as well as the artistry that is "unmissable")
I also want to head over to the rose gardens in Los Bosques de Palermo - where there is a gravel path that goes through the entire park where there is 15,000 different varieties of roses
Dinner at Puerta Cerrada
Saturday:
Visit San Telmo, the oldest barrio in Buenos Aires
Eat brunch late at Home Hotel in Palermo in the morning, then head to San Telmo
Visit the San Telmo antique fair that takes place on the weekend mornings and walk around... maybe purchase some antique souvenirs!
Attend the Open-Air milonga - a tango dance party out in the open air - tables set up at the sides, apps are served with drinks
Stay out late exploring clubs in Buenos Aires
Sunday:
Sleep late and grab some coffee to go and hop a bus back to Cordoba