Fido Lido

Open from May 15 to September 15

(same hours as everywhere else: 9:00 AM–7:00 PM)

Although this beach doesn't have its own website, it does offer training courses for agility and obedience.

In addition, Fido Lido (not to be confused with Lido di Fido - which is in Grado) has showers and a separate access point for dogs to the sea (watch out for the buoys). If you'd prefer to leave your pet here for a while, you can book a dog sitter.
The beach is pebbly, not sandy (which is nice because you won't end up with sand in your car afterward).

The whole thing is a social support project run by an association with 600 members. Residents of the Province of Trieste must pay a membership fee of €60/year (as of 2020) to use the beach, but guests are allowed in for free - though they must sign a guestbook and provide proof of their dog's vaccination history.