The only real driving range I've found in the city so far is "Costa Salguero" in what I believe is Recoleta. It's overlooking the Rio de la Plata and is at the very end of Salguero street. It's southeast of the Jorge Newberry airport if you're checking on a map.
They have a golf course, a putting green, a double decker practice range, two Pro shops, and a cafe. They offer private lessons as well.
Last week I was there and wrote down the following info:
Hours:
Monday 12-22
Tuesday-Friday 8-22
Sat-Sun 8-21
Holidays 8-21
9 Holes:
AR$20 weekend
AR$15 during the week
Club rental: AR$8 (for single club)
Putter rental: AR$4
50 balls: AR$15
100 balls: $AR25
Does anyone know of another place like this in the city?