The Taverna Pub in Ponta Negra has been one of Natal's busiest nightlife venues for years. It is a large, open-sided bar and club that occupies a prominent corner near the beach, and it mixes live music with DJ sets in the Brazilian forró, MPB, and axé traditions. The terrace fills up from about 10 PM onwards and stays busy until well past 2 AM.
It is not a quiet place, but that is not the point. Ponta Negra nightlife runs loud and late, and the Taverna is near the center of it. Drinks are reasonably priced by Brazilian standards. If you want a sense of Natal's social scene rather than just a beach and a bed, this is a reliable place to find it.