The Centro Cívico is Bariloche's main square, it is the jumping off point for your visit to the city. It is the administrative hub (the municipal government building is here), the cultural hub (it's home to both the Francisco P. Moreno Museum of Patagonia and the Domingo Faustino Sarmiento Library), and finally it is the city's main meeting point. You'll see locals here drinking mate, meeting up to go for coffee, to celebrate world cup wins or to protest social injustice.
The plaza has excellent views of Lago Nahuel Huapi in front. It's gates open to Mitre Street, the city's main commercial street.
It is also the meeting point for most tours - like this German Footprint tour.