Although I love to stay at the Fasano Rio hotel whenever I go to Rio, I find that their breakfast is way too expensive, so I prefer to walk to a nearby café.
The best one near the Fasano is the new Terzetto Café.
The new café serves an excellent breakfast. There are 3 options: simples (7 reais, incluiding breads, cake, butter, jam, requeijão), executivo (9,80 reais, includes all that plus juice ) and the huge Terzetto (19 reais, all of the above plus scrambled eggs with sausage).
I had an excellent turkey and white cheese sandwich on pão francês and 2 perfectly-done capuccinos.
I hear the lunch is not so hot, though...
Terzetto Café: Rua Jangadeiros, corner of Visconde de Pirajá, tel. (55-21) 2247-3243.