Praia da Lua
Praia da Lua lies beyond Ponta Negra, upstream on the Rio Negro, so you can make a day of visiting both if you like. To reach Praia da Lua beach, you will need to catch a boat from the marina just past Ponta Negra. You can get to the marina by bus, and then the boat trip to Praia da Lua is about 10 minutes one-way.
Keep in mind that there are places to get a bite to eat or something to drink around the beach at Praia da Lua. It can also be considered more of a short getaway from the busier beach scene of Ponta Negra beach.