Cross the border over to Uruguay (it's easier compared to all other neighboring countries) some few days before your visa expires then re-enter Argentina with a new tourist visa. You can still apply for a 90 days maximum stay period. Colonia, Uruguay is the nearest non-Argentinian city from Buenos Aires and it only takes about 3 hours to get there by ferry.
Visit immigration offices, they are only in Buenos Aires and apply for a visa extension. The visa extension fee is currently AR$600. All you need is AR$ 600 and your passport.
The maximum stay period for all tourist visa holders is up to 90 days, renewal can be done after this 90 day period is over.
If you opt to cross over to Uruguay then re-enter, fly into Argentina, immigration procedures at the airport are easier and faster than those at overland border crossing points.