Madre Rojas is my favorite parrilla in Buenos Aires to recommend as a Don Julio alternative. The quality is chef's kiss. They specialize in wagyu beef (but you can order other cuts for a more affordable option, as well). The side dishes are out of this world (compared to the average 3 ingredient salad on many parrilla menus). I once ordered a mashed potato with leeks that I still think about today, but it will change seasonally.
While "fancy" it is still not overly pricey and you'll still find the place filled with locals. It's a short ride from Palermo Soho but a world apart.