There are no restrictions for foreigners w/o immigration status buying property. There are some paperwork issues like getting a Tax ID number, but its all quite straightforward if you can explain where the $$$ is coming from. As posted above, make sure to get a good Escribano and also someone that can give you proper advice on some taxation issues, including stamp tax, etc.

If you want a flat in the best areas of Buenos Aires, if your maximum budget is US$120,000 you will have to look into units that are 45-60 square meters, and even then it will probably need some work and will for sure not have a parking space in the building.

Premium real-estate in Buenos Aires is now mostly north of USD 2000 a square meter, and more like 2500-2700 per sq. meter if its a new building with complete amenities.