The supreme court is a pretty building at the Praça Alexandre Albuquerque. It may be possible to visit it on the inside too.
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Antiga Câmara Municipal
Built in neoclassicist style with a square central tower, the town hall is one of the finest examples of colonial architecture around. It's still in use. When the doors are open, make sure to have a look inside. There's even some information on the building's history available for visitors.
Palácio Presidencial
Built in the late 19th century as the residence of the Portuguese governor, nowadays it is the presidential palace. It has lately been renovated with financial help from China. Other governmental buildings are located nearby.
Old barracks next to the presidential palace, have seen better days.