Traveling from Rome to Trieste to Zurich during Christmastime - suggestions for places to visit?

You are driving the car from Rome to Zurich? Have you looked at the cost of a car large enough to carry six plus luggage, and the fee for dropping it in another country? You might consider leaving the car while you are still in Italy--generally one-way rentals within one country do not incur a drop fee. Bolzano would work; you can catch the train up to Innsbruck and on to Zurich.

Bolzano has a nice downtown area, but if that looks too big to you, you could ride the train to Bressanone and overnight there. And if you wish to include a village in the Dolomites, go there is the car before Bolzano. Any of the Val Gardena villages would be nice.

Have you been to Venice before? I'd rather have more time there. How long do you have for the whole trip?

I'm not sure how much time you have and whether you've been to northern Italy before. If you have not, I would consider it unusual to stop only briefly in Venice in order to squeeze in Trieste. Trieste sounds interesting, and I plan to visit it the next time I'm in that area, but I believe few would recommend it in lieu of a day in Venice, even if it did not take you farther off the direct route from Rome to Zurich.

The train route from Trieste takes you back to the west, through Venice, Padua, Verona and Milan, then north through Como, Lugano and Bellinzona. The best you could hope for on that ride would be about 9 hours with multiple changes of train.

The shortest driving route is similar. ViaMichelin estimates a bit over 7 hours with no stops. The route through Bolzano/Bressanone would be about 8-1/2 hours. I, personally, would find taking the train more pleasant if I didn't have a good bit of time for stops and wandering along the way. But that's just personal preference. The cross-border drop charge is certainly something to be investigated carefully, however, along with the minimum of 70 euros' worth of tolls and highway vignettes.

Although Bolzano is a good-sized city, it has a very nice historic district, partly pedestrianized, which I really liked. An extra benefit during the winter, when weather can be iffy, is that Bolzano has a number of interesting museums, including the one housing the Ice Man.

Bressanone also has a pretty historic area. The city is, indeed, quite a lot smaller than Bolzano, but so is its historic district, so there's less to do, especially if the weather happens not to be conducive to walking around outside.

I enjoyed my summertime day-trip to Ortisei but have no winter experience in Europe's mountainous areas.

You might want to get a good map and see exactly where you're trying to go. The distances on your itinerary are pretty great--800 miles plus.
From Rome to Zurich is northwest. From Rome to Trieste is northeast--and far out of your way.

You could easily go by train faster and more efficiently through Venice. Trieste is just a few minutes north of Venice and can be easily reached by bus.
You could also take a train from Venice, transfer in Verona and north through the Brenner Pass into Innsbruck.
Trains do go from Innsbruck west into Zurich, too.

From questions asked, it doesn't appear that you've carefully planned for this trip. Have you looked at any guidebooks, like Rick Steves' Italy? I wouldn't begin to strike out in a rental car going over The Alps in winter without careful planning.

You might want to ask experienced travelers here where they'd go--flying into Rome and out of Zurich "X" number of days later.

Once you know where you're going, getting rooms should be simple on Booking.com or other comprehensive accommodation websites.

Thanks to everyone for the input. I was too vague in my initial post. My daughter is studying abroad just north of Rome. She has visited a lot of the areas within a 3-5 hour drive north of her, including Venice. Our other daughter is taking a school trip there in this summer and will spend several days in Venice. The rest of us have already been there as well - that's why I was thinking just an overnight to break up the drive to Trieste.

We have 5 days to work our way to Zurich where we have distant family we will visit. We are then drIving BACK to Rome. On the way home we are stopping for a few days in Milan/Parma area - that is why I didn't ask about an itinerary for a return. Our minivan will be dropped back to the airport in Rome.

I spent a few days in Trieste in October 2015 and really enjoyed it. I stayed at the Palace Suites, apartments booked throught the Hotel Continentale. With a kitchen and laundry facilities they would be convenient for your family, but in the central pedestrian zone, so probably no parking available for your minivan - if it is available it will be expensive. If you decide to go to Trieste, you should take some rain gear, since many of the more interesting sights require you to spend some time outside. With respect to other towns to visit along the way, I agree with others that you could look into Bolzano and Bressanone. The other towns you mention will be packed full of skiers and other winter sports enthusiasts during the Christmas break. It may be too late for you to find decent accomodations in any of them. You would also need to be sure that the person piloting your minivan has good winter mountain driving experience, and is comfortable putting on chains if you hit a patch of stormy weather.