Ponta Negra

This is certainly the most famous tourist spot in Natal.
The village of Ponta Negra is a few square kilometers large. It used to be home for fishers and other working people; around early 1990's, the tourism businesses began to take ove the area; a few years ago, foreigner investors (notably Italians, Portuguese and other Europeans) started to pour money into the area, and tourism oriented businesses flourished.
Today, there are men at work all around the village. Medium and small hotels and flats are being built everywhere (there is no free space for bigger hotels - these are being built along the Via Costeira). Houses are being refurbished and adapted to become restaurants, shops, etc. There are few slots of real estate left (naturally, prices are rising).
However, if the hotels and flats are spread all over, most of the fun happens at the beach strip.
Ponta Negra beach is about 4 km long. In the south end is Morro do Careca, the most famous landmark of Natal. Walking northwards, one first sees about 2km of av. Erivan Franca, crowded with bars, restaurants, hotels, party houses, small shopping galleries, etc; then, the avenue ends, and the next 2km have just a walk way, lined with hotels and some kioskes.

It's not hard to see why this is the hot spot in Natal. 
Morro do Careca is a combination of sea, mountain, dunes and green. Climbing the hill is forbidden, but many people don't care; the gay guides repeatedly mention the lateral trails of the hill as a good meeting point.

Pipa

Pipa is leading tourist destination in northeastern Brazil and is known for having some of the best beaches in the country.
Located 85km south from state capital Natal, Pipa is a small and charming beach village surrounded by immense natural beauty. Tourists from all over the world come to Pipa to experience the amazing mix of paradisiacal beaches, tropical vegetation, colored cliffs, sand dunes, lagoons as well as the famous cuisine and nightlife. Pipa is one of Brazil’s magical destinations – pristine beaches backed by tall cliffs, dreamy lagoons, decent surfing, dolphin- and turtle-filled waters, a great selection of pousadas, hostels, global restaurants and good nightlife. Just another small, roadless, fishing village when discovered by surfers in the 1970s, Pipa today rivals Jericoacoara as the Northeast’s hippest beach town, attracting partiers from Natal, João Pessoa, Recife and beyond at holidays and weekends, and a slew of international travelers year-round. Its laid-back, independent-traveler and ecological vibe still reigns and, with luck, Pipa may be just too small for that to change, despite the ranks of umbrella’s tables along the main beaches catering to vanloads of day-trippers from Natal.
Pipa is small but it can be a little hard to get your bearings on arrival. The main, central beach faces north. At its east end the coastline curves southeast to Praia do Amor. To its west, Baía dos Golfinhos and then Praia do Madeiro curve northwest. The narrow main street, Av Baía dos Golfinhos, runs about 2km through town parallel to the main beach and Praia do Amor, with small streets and lanes running off it down to the beach or uphill inland. The inland ones in central Pipa are, from west to east, Céu, Bem-te-vis, Gameleira, Mata and Albacora (with Arara branching off Albacora). Full-size public buses and tour vans stop at the west end of Av Baía dos Golfinhos; public minibuses and microbuses terminate on Av Baía dos Golfinhos near the southeast edge of town.

Maracajaú

In the city of Maxaranguape you will find Maracajaú beach, roughly 60 km from Natal, and full of surprises, with its crystal clear waters, and its Parrachos de Maracajaú, coral reefs, a short distance from shore.   The reefs are 7 km from shore, but there are many tours that will take you out to see them. Tourism is the main economic activity of this small fishing village with about 2,000 inhabitants and known as the Caribbean of the Rio Grande do Norte, it has great tourism infrastructure. Maracajaú Beach is fun for the entire family, and includes an entire tourist complex known as Ma-Noa, with it's own swimming pools, aquatic park and restaurant.
Directions: Leaving Natal towards the north coast, take the BR 101 towards the Bulls. From Genipabu boards Portal Maracajaú indicate the path.

Pirangi

About twenty kilometers south of downtown Natal, this south coast beach is divided by the river Pirangi, which creates two beaches, Pirangi do Norte and Pirangi do Sul, which are then grouped under the name Pirangi Beach.   The beach is famous not because of the white sands, but because it has the Biggest Cashew nut tree of the World, which is even recorded in the Guinness Book of world records for it's massive size. Due to a genetic issue, the tree has grown to enormous proportions, covering a huge amount of area.
Pirangi Beach do Norte possesses calm waters, ideal for water sports and its sands are often used for sports competitions. Roughly five hundred meters from the shore are natural swimming pools which can be visited via boat tours during low tide. Pirangi Beach do Sul's calm waters make it excellent for families with children, diving and also practicing surfing
During the summer, when night arrives, visitors go to the streets to talk, play and to have fun at the many shows. 
This beach is located fairly close to Ponta Negra Beach, and turns out to be a good alternative to the busy urban beach.  Also near by is Barreira do Inferno, which was a space launch facility. Natal's proximity to the equator makes it a great place to launch satellites. If you're more interested in picking up some souvenirs, try checking out Artesanto Potiguar, which is only a few kilometers away from here.

Genipabu

Genipabu (or Jenipabu) is a beach with a complex of dunes, a lagoon and an environmental protection area located in Natal, one of the most famous post-cards of the Rio Grande do Norte Brazilian state.
Genipabu is internationally famous for its natural beauty and for its "buggie" and dromedarie rides. With its beautiful and calm waters, it attract lots of tourists in the summer.
Its huge dunes and fresh water lagoon are a major touristic destination. The beach has plenty infrastructure of hotels, inns, restaurants, beach tents, "buggies" rides, rafts and dromedaries.
A sport that is played in the dunes around the lake is the "esquibunda", in which a person slides the dunes with a wooden board.
"Buggie" rides are offered locally in two styles, com emoção (a riskier ride) or sem emoção (a safer one). It is urged, however, that only authorized professionals responsible for security of both tourists and environment should be used.
The dunes of Genipabu are movable, because the hard winds in the Rio Grande do Norte coastline moves the sand from one point to another, shaping the landscape.