Hiya
4 weeks in South America unfortunately isnt a lot of time if you wanted to get from BA all the way up to Peru and back again. It's doable if you fly I suppose, but my advice would be avoid doing that and just spend your 4 weeks around Argentina/Brazil.
Buenos Aires alone is worth many weeks! but my advice would be spend a week there. It's a great city and there's so much to see and do.
Option A
From there, one suggestion would be to travel north to Iguazu Falls (one of the major sights worth visiting in South America). That's situated on the tripartite borders of Argentina/Brazil/Paraguay, so you could even take a quick trip over into Paraguay if you felt like it.
Onward from Iguazu, it's about a 20hr bus trip to Rio de Janeiro - probably the most exciting city I visited in South America. I just loved it. Spend a few days there and then loop back down to Buenos Aires, stopping at the island of Ihla Grande, maybe Florinopalis or Porto Alegre, crossing into Uruguay and finally getting the ferry across to Buenos Aires.
This trip is doable at a comfortable pace over the space of 4 weeks and you'll cover two of the best cities in the world, beaches, jungle, waterfalls and islands.
Option B
From Buenos Aires, you could do a round trip across Argentina to Santiago, Chile and back, stopping at Cordoba and Mendoza - two great cities but very different. Cordoba is in the heart of the country and has a real student vibe, really friendly ppl, lots of good bars and restaurants and is right next to the Sierras. Mendoza is situated in the foothills of the Andes and is all about the vino!
Plus, if you're a climber/hiker, you could attempt Aconcagua!
The bus ride from Mendoza across the Andes into Chile is spectacular at any time of the year!
That round trip could also be done pretty comfortably in 4 weeks.
Option C
You could fly from Buenos Aires to Lima I suppose. From there you would have to get to Cusco, about 10-12 hr bus trip. You need to spend a few days in Cusco acclimatising to the altitude before you would attempt the Inca Trail, so this is something to take into account if you are caught for time.
Following that, you could make your way across into Bolivia, cross over to Salta, Argentina and travel down through Northern Argentina and back to Buenos Aires.
I think you would find this trip much harder to accomplish in 4 weeks, but it's not impossible. 
Hope that helps a bit.
Ev