A 15th-century castle and fortress on the San Giusto hill, now a museum of historical weapons and local history. The views over the city and the Gulf of Trieste are the main draw — panoramic in every direction, and worth the climb even if you skip the museum interior.
The courtyard entry (€1) is the budget option if you just want the view. Combined with a walk up the hill and a visit to the adjacent Cathedral of San Giusto, this makes for a rewarding afternoon away from the waterfront.