Short time/ teenagers

With such a short amount of time I'd just stick around Rome. There is lots to do there. Maybe take a day trip or two if you really have to get out of Rome for a bit. Ostia Antica or Pompeii. Orvieto is only about an hour away by train.

They might enjoy biking out to the Via Appia Antica and Aqueduct Park. There's also a Museum of the Walls near the Piramide where they can walk a section of ancient Roman wall. Check the roninrome.com site for more ideas.

Suggest you stick to Rome. The 23rd will not be a full day. You might be late in arriving and / or jet lagged. The 28th is not a full day due to travel to the port. That only leaves four full days. One side trip to Ostia Antica and the other 3 days will just let you scratch the surface of Rome.TC

I agree with sticking to the area around Rome. Rather than cramming everything into 2 days, I would mix up the museums/churches with some of the suggestions below to create more fun variety. Pompeii is a great suggestion, plus you can hike up Mt. Vesuvius if you are an active sort of crew. Canoeing on the Tiber Segway tour of the city (may have an age minimum) Rent bikes or pedal cars in the Borghese Gardens Attending a soccer match would be fun, but I think you're a bit too early to catch the season. You could check it out. Attend an opera at the Baths of Caracalla. Even if you don't think you are opera fans, there's nothing like seeing the spectacle set in Roman ruins.
*Organize a contest to determine the best pizza or gelato in Rome. Parents are not allowed to identify contestant shops. The kids must choose and sample accordingly. Tip: use jetlag to your advantage by seeing St. Peter's the first day you arrive. You will all wake up super early. Arrive at St. Peter's at 7:00 am. There will be no line and you'll have the place to yourselves for an hour or so. Be sure to climb the dome! And my best suggestion is to hand your kids the guidebook and let them each pick one thing they really want to do. This helps them own the trip, not just follow along after their parents, plus they get to do something they really want, not just the "must do's."

You're right about spending at least a few days in Rome. There is plenty to fill your entire time before the cruise. It doesn't seem like you have enough time to really get up to Venice. I'd say you have maybe three nights (two days) to spend elsewhere. That's enough for a train trip south to see Pompeii/Naples or a trip north to visit Florence, not enough to do both. If you choose Florence. Orvieto is a good Umbrian hill town that is convenient by train between Rome and Florence where you could stop. It offers more than most hill towns, including tunnels that date back to the Etruscans. The problem is Florence is best for art, sculpture and architecture and may not appeal to teens - climbing the dome, seeing some Medici palaces, or visiting the nearby science museum to see Gallileo's finger may be interesting. If you choose north rather than south, you can always spend part of a day at Ostia Antica for a look at extensive ruins of a Roman city.

Regarding the Segway Tour (Which the kids will LOVE), minimum age is 12, so you're OK. The Segway will take you down narrow streets that you otherwise wouldn't be able to do via taxi, etc., Agree, that there aren't enough days to do much other than Rome -- but Rome is Awesome! Go to Campo di Fiori for gifts/flowers/and condiments that you can take home. I pack zip loks and use those to "double bag" to take home. They also sell salami, etc., t-shirts, and a million other things there. I think your kids won't be bored in Rome at all! Do one day trip, and you'll be fine.

The Catacomb tours are fun. There are also several beaches (freshwater lakes and the Mediterranean) a 30-45 min train ride from Termini. July is hot!

Thank you all for the great ideas. I think Pompeii day trip will be the winner. And maybe the Segway tour- I'm laughing at myself already