Museu de Ciência e Técnica da Escola de Minas

In the old governor’s palace above Praça Tiradentes, this museum features dazzling gemstones from around the world. Even if you skip the museum itself, it's worth climbing to its front terrace for spectacular views of Praça Tiradentes backed by mountains. The attached astronomical observatory offers free shows between 8pm and 10pm on Saturday nights.