Puri Saren Agung is also known as the Ubud Royal Palace and is close to the Ubud Art Market so you can easily take in both places at the same time. It is located in the center of the city and dates from the 1800s when it was built during the reign of Ida Tjokorda Putu Kandel.
The Royal Family still lives in sections of the palace which is also used for ceremonial reasons but you can still walk around the gardens here and enjoy the Balinese ornate architecture. It is also known as the best place to come in the evenings if you want to take in a traditional Balinese dance performance.
(Source: https://www.thecrazytourist.com/25-best-things-ubud-bali)