The Castello di San Giusto and the Basilica di San Giusto are worth a visit. Located at the top of a hill that was the center of the city in Roman times, the views from the ramparts of the Castello are marvelous, and there are some lovely mosaics in the Basilica. It's a manageable uphill walk from the center of town if you're in decent condition, and I understand a bus goes up there as well. If you planned carefully, you could probably get out to the Castello di Miramare, the seaside palace of the ill-fated Archduke Maximilliam, before closing time. It's a short city bus trip from the center of town. There are several city museums which are worth a visit if you're into 19th century furnishings. If you're not feeling ambitious, the center of town is a pedestrian zone, and it's fun to just walk around. The Piazza dell'Unita - the large waterfront square - is worth a visit at night (perhaps for an after-dinner espresso) when the big neoclassical buildings framing the square are lit up.