Che Juan Hostel is the most recommended hostel among my Facebook group. They have dorm rooms (with privacy curtains on the bunks) and private rooms. With a complete kitchen and social spaces this is ideal for budget or social solo travelers looking to meet fellow travelers.
It's in Microcentro, an unusual location that's more catered to offices, but the location offers the advantage of being a stone's throw from San Telmo, Puerto Madero, the Casa Rosada, and Obelisco. From here the Subte can buzz you into Recoleta and Palermo in just 10 minutes.