If you have only a few days to spend in Rio de Janeiro, here are the must-do's in descending order:
1) Hiking up the back of Pao de Acucar.
Most people wait in long lines to ride the touristy cable cars that pull you up the side of the mountain. However, if you are the adventurous type, get out your hiking shoes and get ready to get dirty. There is a walking path that leads from Praca General Tiburcio (where you catch the cable cars) to the base at the back of the mountain. The path runs around the smaller Morro de Tijuca and then around Pao de Acucar itself. A large pillar stands at the end of the paved walkway to block further travel.
But here is where the fun starts. Walk around the left side of the pillar and you will discover a rudimentary hiking trail. Follow this trail and always go up when possible. After a while you will encounter sheer rock, up which you must scamper. Follow the imaginary path (just take the route that's easiest) and you should come to some bolts stuck into the rock. Follow these bolts up (there is some pure climbing here but you won't need equipment - just a big pair of Brazil nuts) until you find another trail in the brush. This trail will lead you up to the main tourist center.
Caveat: you probably won't want to climb down, as the climb takes about 1.5 hours. You also can't buy a ticket going down from there, so you should buy a one-way ticket before you climb up. After taking the cable car down to Morro de Tijuca, you can hike down again (well-defined trails).
2) Walking down the entire length of Copacabana and Ipanema beaches.
I can't stress this enough - walking down these beaches gives you a great taste of the carioca lifestyle. People flock to the beaches at all hours of the day (more so around 10am) to soak up the sun and to show off their stuff. You might even meet your own girl from Ipanema.
3) Exploring the Parque Nacional da Tijuca.
Endless hiking and exploring opportunities are available in this pristine forest. Waterfalls, ravines, exotic butterflies, monkeys, and thousands of birds all make this place an assault on the senses. It's hard to believe that you are actually still within the city limits. This place is so immense that you may even get lost if you're not careful.
4) Walk through the Copacabana neighborhood.
You will find numerous little shops and great restaurants (some of the best were on Avenida NS de Copacabana, such as the Kilosaurus self-service). You will rub shoulders with the high-class people and feel the richness of the city's lifeblood.
5) Go see Cristo Redentor (Christ the Redeemer).

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View of Corcovado mountain from Baia de Guanabara
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Yeah, it's touristy, but the sight of it is awesome nonetheless. Standing on top of the Corcovado mountain, the gigantic statue raises its arms over the city to protect it from evil. Plus the view from up there is breathtaking.
Questions?
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