The Jardim Duque da Terceira is the main public garden in the center of Angra, a formal 19th-century layout of paths, exotic trees, and a bandstand enclosed by old walls. The garden occupies the site of a former convent and retains a sense of enclosure that makes it feel like a room in the city rather than a civic afterthought. In the afternoon, when the sun gets serious, it's one of the better places in Angra to sit under shade.
The planting reflects the Azores' position at the convergence of Atlantic climate zones: hydrangeas (which line virtually every road on Terceira), camellias, subtropical palms, and various specimen trees that wouldn't survive on the European mainland. The bandstand at the center occasionally hosts concerts in summer; check locally for the schedule. The garden connects to the network of streets near the cathedral and the main square, making it a natural pause point on a walking circuit of the historic center.