Florence, Venice and Cinque Terre

Stay in Tuscany in a villa with pool, do Florence as a day trip. Or visit Umbria instead of the above. For your first visit I think the Tuscany plan is best. Look at the Chianti region for proximity to many charming towns a as well as Florence and Siena.
Venice is unique! Stay in a neighborhood away from St Mark’s.
I am offering all of this with your children in mind.

Cinque Terre will eat up many hours on a train when visiting between Florence and Venice, so I would look at the logistics before deciding to include it.
Some villa rentals have a one-week minimum. Get a good Tuscany/Umbria book to see what appeals to you, as there are probably hundreds of options. If you can narrow down to the area, you'll get more targeted responses. Many recommend Fiesole as a more suburban place to stay within easy reach of Florence.

Venice is unique, there is no other floating city teleported untouched from the 18th Century. Unfortunately what makes Venice unique also makes it crowded during the day. When day-trippers have finally left, walking around and getting lost is awesome and unforgettable.
The Cinque Terre are nothing special to Everyone but German hikers, Rick Steves and his followers.

Fly into Venice, stay there a few days and Train to the Cinque Terre via Milan. Then Take another train to Florence.

Seeing both the Cinque Terre and Venice eats up a lot of time for transfers, just look at a map. The Lake Como could be an alternative: Milan MXP airport-Lake Como-Venice-Florence-Villa in the Countryside-home.

If you don't want to see Rome, you can fly home from either Florence or Pisa.

For first time travellers, there isn't a huge difference between the Umbrian and the Tuscan countryside; I am afraid You'll have to distance yourself from Florence to find the kind of Villa with a pool you seem to be interested in. This means you'll have to rent a car, get an IDP, learn about ZTLs etc.

As the father of a 12 year old girl, I'd opt to soak up Florence over Tuscany or Umbria. As lovely as the countryside is, it could be boring for the kids. We spent a week enjoying Florence from a fantastic AirBnB in the Oltrarno neighborhood. (Search for "Airbnb Luxury home in downtown Florence Emanuela") Perhaps as idyllic as your vision of a villa with a pool is the beach in Cinque Terre.

Happy planning

Hi Amy - welcome to the forums!

Backing up a bit? 'Fraid there's no such thing as a "must see" unless it's a must-see for YOU. The problem here is that, beyond sitting by the pool at a villa somewhere with pleasant scenery, we don't know what else it is you want to do and see in Italy. Surely you don't want to spend 12 days just sitting by the pool? 😉

My personal must-see list for Florence is long as my arm - I don't recommend it as a day trip as there's much too much fascinating ground to cover there! - and we'll be going back to do even more than we've done. Additionally, my husband and I are not "villa" types; we'd go bugcrazy after 1 day, and like to be closer to the sorts of things we go to Europe for, the things we can't see/do at home: the museums, archeological sites, glorious churches, architecture... The things you and your family want to do/see may be very different and that's OK; it's your trip and not mine!

But we can't advise if Venice is a "good" destination for you without knowing if you're interested at all in what she has to offer. Same for Florence. Dario covered some of the considerations around the villa-with-a-pool thing so yes, you'd want to read up on the ins-and-outs of driving in Italy as a car might be a necessity for that particular wish-list item. We prefer using the trains so that's another reason why we don't do agriturismi but again, to each their own as long as it suits their particular travel style and they know what they're getting into.

So what I'd do? Go to the library and check out some guidebooks, and do some browsing around on the net for what Venice and Florence and the CT have to offer. If you and the family find those things interesting, then you're good to go, If not, you might want to look at other locations. You could also tell us a bit more about what your family might like to see and experience in Italy so we can offer advice more suited to your interests?

You all might also - as a family, or in clusters - watch some of Rick's TV shops and travel clips, right here on this website ("Watch, Read, Listen") in order to get a better sense of Tuscan countryside, the Cinque Terre, Florence, Venice, etc. Your kiddos might enjoy watching and chiming in about what appeals to them. (When I took Daughter #1 to Rome/Florence/Venice when she was 13, and then later Daughter #2 to Paris/Bayeux/Mont St Michel at age 12, I made a deal with them: time in museums/churches would be more or less equal with time shopping/cafe sitting/people-watching. Your girls may or may not have the same interests as mine did at that age....)

Venice is unique, there is no other floating city teleported untouched from the 18th Century.

Dario is spot on. His suggestions make a great deal of sense.

Get the daughters involved in the planning. Much less likely to become unhappy campers if they can take part in the planning.

Seems to me Venice would be great for your family for a couple of days. Florence is also fabulous and I like your villa/pool idea! It's my understand there are some great day trips from both places as well.