Hostel that everyone can and does recommend! Yes, it's The Adventure Brew Hostel, the first real backpacker hostel in La Paz! 

The Adventure Brew Hostel's modern main building and its colonial little brother, The Brew Too, were created to give you, adventure traveler, a friendly and fun base from which to plan your explorations of Bolivia, take a break from your travels, meet other travelers, or just to recharge your batteries before heading out for further adventures. We have taken travelers' best ideas and put about everything a backpacker could want from a hostel under one roof.