Trieste’s cathedral is on a hill overlooking the old town. You can get up by car (by help of a navigation system or supernaturally good instincts), by elevator from a parking garage at the foot of the hill, or via a long flight of stairs, shaded by old trees.
I used the elevator, but if you have enough time for the walk and are able and fit enough, I’d recommend the stairs. On your last meters to the right, you’ll see the entrance to the Lapidario, basically a collection of ancient stone fragments, mostly of Roman origin, I suppose. But then, I skipped it, and when I look at the video on the Orto Lapidario‘s site, I certainly regret it. Next time 🙂