Mirante Dona Marta is one of the best viewpoints in Rio de Janeiro. From here, you can see almost the same view as you have from Christ the Redeemer, but for free!

Mirante Dona Marta faces the Sugarloaf Mountain and is one of the best spots in town for watching the sunrise.

PS: There is no public transport that goes all the way up here, so if you take a taxi, make sure you arrange the drive back as well because there is almost no phone signal at the viewpoint! Read the guide for more tips.