For visiting this and the cathedral would recommend parking in the underground car park on the main road into town at Parc De La Mar before the port. Not cheap but not ludicrously expensive (cost around 1.7 euros an hour) and saves you having to battle town centre traffic, step out next to the park with fabulous views and short walk to the cathedral and palace.
The palace is expensive at 9 euros and 4 euros for the audio guide which for my money did not give enough information - around 30 seconds for each room with minimum detail as to actual age of works of art or any insight into renovations over the centuries - still confused by history of building!
However what was there was impressive with chance to go onto the terrace with amazing views of the port and parts of the town. Some very good Flemish art pieces but poorly lit and found myself with nose almost on the canvas to make out details of painting!
Amazing ceilings of a style I had not seen before and a medieval fresco plus tapestries that deserve some study, the borders contained detailed portraits of various animals - better than the main subject for me!
Nice photo opportunities in the courtyard but be aware that as well as an official royal residence this is an army base.
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