If it's sunny, visit Sugar Loaf or Corcovado as soon as you arrive in Rio de Janeiro, to make sure you see the city from above. There is often a chance of cloudy, rainy weather in Rio, even in the winter, when the weather is drier.
A tip: when you're pressed for time, as when you visit Rio on a weekend, it's better to visit Corcovado if you're taking a bus. There are more buses to Corcovado from the beaches than to Sugar Loaf. Some bus lines like Linha 569 and Linha 570 go by most beaches and to the Corcovado access (on Rua Cosme Velho).
If you go to Corcovado, save one hour to visit next-door International Museum of Naive Art of Brazil.