The Strada Vicentina, often called the Napoleonica, is one of Trieste's easiest rewards: a broad, mostly level walking route cut along the Karst edge above the city. The path gives you repeated views over the Gulf of Trieste, the port, Miramare, and the limestone plateau behind you.
Go for the light rather than for athletic glory. Late afternoon is especially good, when the sea turns silver and the city begins to look less industrial from above. It is also a useful way to feel how sharply Trieste changes once you climb out of the streets and into the Karst landscape.