The city hall (Câmara Municipal) faces the Praça Velha — the Old Square — which is the social and geographical center of Angra. The building has medieval origins but has been rebuilt and enlarged multiple times, most recently after earthquake damage; the current facade is handsome without being exceptional. The square in front of it is the more important feature: lined with café terraces and flanked by the cathedral on one side and the former convent buildings on others, it functions as the living room of the city.
The Praça Velha is the right place to orient yourself when you arrive. The surrounding streets of the historic center radiate from this point, and the café terraces give you a place to sit and get your bearings. On weekend evenings and holidays the square fills with residents in a way that feels genuinely communal rather than staged for tourism. The city hall itself is open during business hours and the public rooms on the ground floor are worth a brief look — the council chamber contains paintings related to Angra's history and a strong sense of a civic institution that takes itself seriously.