Though a little run-down, historic, residential Catete and Glória are well worth an afternoon's sightseeing. The Palácio do Catete, the presidential palace until the government moved to Brasília, itself warrants at least two hours. In addition to its hilltop church, Glória has a lovely marina that's perfect for a picnic or stroll, especially on a Sunday, when the main road is closed to traffic.
Handily located on the metro line between the Zona Sul and Centro, the two neighborhoods' subway stations are just a few minutes' walk from each other. From Ipanema or Copacabana take the 10-minute ride to Catete, and you'll emerge right in front of the Museum of the Republic. Set aside a couple of hours to see the exhibits and enjoy a coffee in the gardens before taking a stroll down to Glória's marina, taking in the monument to fallen soldiers. The surrounding area can be a little rough, so jump on a metro to Centro or the Zona Sul when you're done sightseeing.