Niterói:
Located on the other side of the Guanabara bay, this city has magnificent views of Rio de Janeiro, besides that it has attractions the worth a day visit such as the Contemporary Art Museu (MAC) ultra modern building designed by the brazilian architect master of modernism, Oscar Niemeyer; Fortress Santa Cruz lying on the entrance of the bay with gorgeous views over the Sugar Loaf and the mountains of Rio; Parque da Cidade, city park lying on a mountain with several great lookout points and the fish market of São Pedro, traditional indoor market where you can buy, shrimps, fishes, etc. for very cheap prices and eat it there on the restaurants on the second floor.

Petrópolis:
Distant 70km
(44miles) from Rio, lying beautifully on the mountains of Serra dos Órgãos,
once was this town the favored getaway of the imperial family. The many
elaborate 19th century buildings in the old downtown area form the
central attraction of Petrópolis, with the highlight being the old summer
palace itself, now the Imperial Museum.
A historical walking tour can be done visiting the French neo-gothic Cathedral, Rio Negro Palace, Casa de Santos Dumont Museum, Palácio de Cristal and having lunch in one of its cozy restaurants.