After you fly in to Trieste, you can buy a bus ticket for 4 Euro that will take you to the city. We had a decent lunch at a small restaurant a few blocks from the bus station. We only had 3 or 4 hours before we could get a bus to Rovinj, Croatia. It was about a 40-minute walk from the bus station to the sea. There wasn't much of a beach, and the walk was all through industrial and rail road area.
We hadn't heard good things about Trieste, so we didn't give it much of a chance. But from what we did see, It's not a destination that I would recommend. But it is centrally located, and flying there is CHEAP. I think I paid less than $80 for two tickets from Paris to Trieste. It is an economical way to get to Slovenia or Croatia, and see some real beauty.
Sky Scanner is the website I used to book most of the flights. It is one of the only sites I found that will allow you to search for the cheapest flight from a specific airport to anywhere in the world. Its basically built for aimless jetsetters like us. I recommend it.