Generally, exchange rates are better in the city than at the airport, and cash gets better rates than traveler's checks. Most Brazilian banks don't exchange money. One that does is Banco do Brasil. The branch at Galeão offers good exchange rates, but it won't provide credit-card advances.
Casas de câmbio (exchange houses) are found all over the city, especially along the beaches and on Avenida Nossa Senhora de Copacabana and Rua Visconde de Pirajá in Ipanema. Many change money without charging a service fee. Sometimes, depending on the amount of money you wish to exchange, exchange houses have a better rate than the banks. American Express is another option.
Some hotels, such as the Caesar Park and the Copacabana Palace, offer competitive rates but charge a commission if you're not a guest. On weekends hotels may be your best bet, because few other places are open. Or try the Banco 24 Horas automatic teller machines (ATMs) throughout town, which dispense reais.
American Express (Av. Atlântica 1702 B, Copacabana. 021/2548-2148 or 0800/702-0777). Banco do Brasil (Rua Bartolomeu Mitre 438 A, Leblon. 021/2512-9992.) Banco 24 Horas ATM (Av. Nossa Senhora de Copacabana 202.) Casa Universal (Av. Nossa Senhora de Copacabana 371 E, Copacabana. 021/2548-6696).