Location is one of the most important factors when picking a hotel, short-term vacation rental or, in this case, a hostel. If you can't make your mind up between Palermo or San Telmo, why not choose a place smack in the middle: the Microcentro? There, you'll find the V&H Hostel Club, right around the corner of the Teatro Colon and the Obelisk. Great public transportation options right around the corner make it easy to visit all of Buenos Aires' many sights.
If the working class vibe of San Telmo isn't your thing, and you're looking for a hostel in the more upscale Palermo, check out Kapaké. Found in the relatively quiet neighborhood of Palermo Hollywood, it's got a great location, near the parks and the subway station. Fitting in perfectly with Palermo, the Kapaké Hostel is fashionable and cool; a comfortable little spot which prides itself on cleanliness and safety.