You don't really mention your priorities or interests but Verona is a chic, mostly pedestrian, cafe culture like city the bend of the river centered around the old Roman core that feels smaller (to the tourist) than it's size would suggest. It has an intact Roman Arena, Theater which are still used for music with music and opera being a big part of the city's summer schedule. It also has several interesting churches and smaller museums to explore. Day trips include Bologna (also a good candidate for a stay if you want a bigger city), Padua/Padova, Brescia (Roman ruins), Vicenza (Palladian architecture).
Be aware that Trieste weather can be rugged in the winter months and their season is shorter than most of Italy being in the very north and at the end of the Adriatic Sea so scheduling there is important. Also be aware that Trieste is faster to reach by Venice via bus versus the train which swings further north to Udine. There are also dedicated transfer services from Venice to Trieste that many people use.
Much of the tourism in Verona is German and I would classify both Verona and Trieste as being more "European" cities than just Italian cities and Venice is it's own thing out of time and space so while this won't be the most "Italian" of vacations it sounds interesting.
You might also consider the lakes of northern Italy as alternative waterside vacation versus the Adriatic since there beautiful and aquatic in their own way. Lake Garda is the closest to Verona and Venice and may fit what you're looking for.
Have a great trip,
=Tod
