* The main square, the only one in Italy directly facing the sea.
* Parco di Miramare, one of the most beautiful in Italy featuring the Castello di Miramare.
* Take a walk from Grignano (close to Parco di Miramare) down to Barcola and enjoy the atmosphere.
* Villa Revoltella could be a nice place for a walk/picnic in summer.
In the outskirts of Trieste, you can also visit:
* La grota gigante - a big cave, and then have something to eat in a nice place nearby.
* Sistiana-castle of Duino. ***Amazing place!
* Muggia, 30 minutes from Trieste. It is a cute small town. about 7 years agoAnswered by lefft via WorldNomads.com
Do not forget to visit "Castle of San Giusto" together with the old romanic Church and romanic rests (it's on a low hill in the city centre.
Then right in the center the old romanic anphitheather.
Have a walk around and look at the buildings archictecture.
Take a bus to the hills around Trieste and have a relaxing walk on "Napoleonica Trail" with a wonderful view of the city and the sea. about 7 years ago