Both the Serra Verde Express [1] line and the Estrada da Graciosa pass right through the Parque Estadual do Marumbi (tel. 41/3462-3588, www.cosmo.org.br [2], 8 a.m.–6 p.m. daily, free). Aside from feasting your eyes upon virgin Atlantic rainforest, you can scale mountains and bathe in waterfalls.
The park offers plenty of well-marked hiking trails, many of which were carved out of the wilderness centuries ago by Indians and early settlers. One of the easiest is a 45-minute trail that leads to the hilltop of Rochedinha, with stops for bathing in natural pools created by the Rio Taquara.
More adventurous souls can climb to the summit of Monte Olimpo, which at 1,539 meters (5,049 feet) is the highest peak in Paraná [3].
The Serra do Mar Express stops at Marumbi station, which is within the park. At the entrance is a visitors center with maps of the trails and other information. The park is also accessible by bus from nearby Morretes [4].
Links:
[1] http://www.moon.com/destinations/brazil/the-south/parana/curitiba-paranagua/the-serra-verde-express
[2] http://www.cosmo.org.br
[3] http://www.moon.com/destinations/brazil/the-south/parana
[4] http://www.moon.com/destinations/brazil/the-south/parana/curitiba-paranagua/morretes