Brazil is a massive country and would take a great deal of time to do in it's own right. Many people just get to sample Rio or some other places (see below)
City Guides Rio De Janeiro
Things to do in Brazil: Learn to Surf, Horseback Riding, Amazon Tours, Visit Favelas, Amazing Beaches, Amazing Nightlife, Waterfalls galore, Exclusive Luxury of Fernando de Noronha a most exclusive address.
This is not the full list but we are choosing those places that you might start to consider as being the best and most popular places to visit in Brazil.
Rio de Janeiro is a vast and exciting city. You should certainly plan ahead for where to stay and what you might like to see. With something for all tastes the city could be the most attractive travel hub for other parts of Brazil and may well be your entry point with many options for flights into the country.
In the north of Brazil is Bahia and Itacarè where you will find a very real Brazil and its a great backpacking destination it's especially popular as a place where you can learn to surf or even try it as the waves are nicely tame and predictable. The region is rich in culture for others and you might like to take some time to explore towns and beaches nearby. Salvador would be such a town and deserves a separate mention.