Brazilians come to São Paulo because there is work. It's full of skyscrapers and pollution, and not easy for a casual visitor to access, whereas Rio will grab you from the first moment with its culture and music and beautiful views. With just 10 days to get the unique flavor of Brazil, I would arrange to fly directly into Rio, and if not possible, leave for Rio immediately. You could get the bus up the coast to Paraty and spend a day or so of beach time at Trindade. Beach towns are usually pretty lively (depending on time of year of course). Go on to Angra dos Reis and get a ferry to Ilha Grande for a few days. Then ferry back and continue on to Rio on Costa Verde busline. (
www.ipanema.com gives a good overview of Rio--neighborhoods, clubs, etc.)