One of the things that keeps amazing me about Rio is the presence of nature within this 6 million people city. JB is a place where that feeling is enhanced. You feel the forest and the collection of trees is astonishing. The entrance costs 6 r$ which is cheap, because it is an institution run by the Government.
There is plenty of things to see. Three house with bromelias, orchids and "carnivore plants".
Huge water lilies, mini monkeys like the ones in "Rio" - they are called "mikos".
And sometimes the bigger, brown capuchin monkeys come down from the forest and swings by. There's a japanese, well-kept garden and the alleys with the "Imperial Palm trees".
There is a kids <10 years playground with a café and a small pond. And my favorite bakery La Bicyclette has a franchise within the reception area.
Bonus info: There's a back entrance from Gavea and one from Horto.
Bonus info 2: Elderly people can have a tourist ride around the park. Must be reserved at the visitors centre - reservations only on the day of the visit.