Trieste tourist office publishes a useful map of the network of numbered footpaths in the Carso; it shouldn’t be used for serious navigation but is a good guide. For serious hiking in the hills you need Tabacco’s Carso Triestino e Isontino Map #047. Two walks near Trieste can be particularly recommended:
The Strada Vicentina Also known as the Napoleonica, the Strada Vicentina is some 3.7km long, contouring the hillside above the city, between the Obelisco campsite, 7km from Trieste, and the hamlet of Borgo Nazario (near Prosecco). It’s a scenic, easy walk, partly shaded by trees and partly cut through by almost sheer limestone cliffs; on a clear day the views are superb. Access to the Strada Vicentina is easy: Obelisco is a stop on the tranvia, and the Borgo Nazario end is near Via San Nazario, where the #42 bus stops on its way back to Trieste station.
The Val Rosandra A miniature wilderness of limestone cliffs and sumac trees, the Val Rosandra is the local rock-climbing headquarters and is crisscrossed with walking paths. From the bus stop at Bagnoli Della Rosandra (bus #40 from Trieste), follow the road behind the square to Bagnoli Superiore where the marked hiking trails begin. Highlights include the remains of a Roman aqueduct, the little sanctuary church of Santa Maria in Siaris, and various pools and waterfalls. If you get as far as the tiny hamlet of Bottazzo – the last habitation before Slovenia – you’ll see a sign indicating a friendship path linking communities on either side of the frontier.