Trieste is not likely on the radar of any American planning a trip to Italy. I only passed through and spent two nights because it made for an easier route from Rijeka to Piran - Trieste's the largest city in the area and acts as a hub for inter-country travel. The city is two hours northeast of Venice and before arriving I was questioning how Italian Trieste would be considering it's almost surrounded by Slovenia. It turns out it's still very Italian, there's a noticeable buildup from Croatia in the sense that the city feels both old and modern, both quaint and cosmopolitan, and it's nice that it's not on many travel itineraries, it feels like a local version of Italy where the streets and sites are trampled with other tourists.
It feels more Italian than Croatia. There's a decent waterfront area.
Barcola isn't the greatest beach, if it's a beach at all, but a good place to see locals.
Miramare Castle qualifies as the major tourist site - not too crowded but worth checking out on the way to/from Barcola.
James Joyce lived in Trieste for quite some time in the early 1900s and where he began his career as a writing. There's a statue of him near the waterfront and the image to the right is a coffeeshop he wrote in. I unfortunately had no burst of creative writing while in Trieste.
You can take a tram up to a hill park with good views of the city.
I'm selling this a bit short because I'm writing this over seven years after I visited but I recall Trieste being a good spot - primarily because it had the food, old buildings, squares, cafes, etc. that you'd be looking for in Italy but none of the crowds.
For additional photos see FLICKR ALBUM.