If you are not lucky enough to be visiting the real jungle in the interior of the country, then a good substitute for a day trip is the last remaining area of forest close to the city, the Parque Nacional da Tijuca, which is around 15minutes from the city centre, and provides a good chance to see what you are missing. Regular buses run to the jungle, and there you will find almost virgin territory, where the screams of animals echo through the dimly lit pathways between the trees, and you will see many wild animals.
Sugarloaf mountain is best visited as the sun sets, and from the top, the views of the city lighting up for the night are nothing short of spectacular. The top of the mountain is easily reached by cable car, although more active tourists may want to climb to the top of the 396m tall hill.