The Brazilian real is fairly strong against the U.S. dollar, and Brazil's biggest cities are just as expensive as any city in the U.S. To reach Rio de Janeiro or Sao Paulo, the lowest-priced flights often originate from Miami. Once in Brazil, buses get you around cheaply. If you don't mind bunk beds and bedlam, try the hostels or albeurges in Rio, some only minutes from the beach. Consider a pousada, a family-style bed and breakfast, for budget lodging ranging from quaint to rather rustic. Street vendors offer a bargain alternative to restaurants. In Salvador da Bahia, try the acaraje, or bean patties, or sip an acai smoothie in Rio.
For the Amazon, in northern Brazil, high season for tourists is July through September, when there's less rain and fewer mosquitoes, but March through June is a cooler period. December through May is likely to be quite rainy. High season in Rio de Janeiro is the Southern Hemisphere's summer, December through March, and brings crowds and high hotel prices. Carnival, usually in February, will be very crowded, loud and festive. May through October is a good option for lower prices, but there may be some days that aren't particularly beach-friendly. It's warm enough for the beach nearly every day in the northern coastal region, but rainy April through May, so there are fewer crowds then.