Italy and France

Hi there. Your itinerary is very doable by train - I have been to all of those places, some more than once. I trained in 2017 from the Italian Riviera (Cinque Terre) to Nice and eventually to Paris (I stopped in Provence for a few days between Nice and Paris). I would point out that some of these trains will be expensive train tickets if purchased near the last minute - I would try to book them as early as possible online to save money, if you can lock yourself into non-refundable non-changeable tickets. Tickets aren't on sale for the summer yet. Try the Trenitalia website for Italian train tickets (a rival company is called Italo, has trains on some routes). For the French trains, try the SNCF website.

I don't know what you and your daughter are interested in. Would she really have no interest in Florence to the point that you would want to skip it (but you do I know)? Nice is a beach town - if getting our beach time at peak summer season is one of the goals of your trip, you can certainly do it there, but there is so much to see in Italy (and France) that I might suggest curtailing your time there or skipping Nice altogether in favor of more Italian cultural experiences. Of course...it's your trip, you and your daughter know what you want to see and do, so if that's what you both want to do, then of course do it.

Florence makes a convenient base for Siena and other day trips - if you want to stay there the entire four nights, that's fine. Some people hate to change hotels often so they would prefer a base for four nights vs. splitting it up between two cities. Personal preference. Siena is a wonderful city - I only day tripped there, when it was pretty crowded with tourists and have been told it's much more pleasant at night. But there's really no right or wrong answer here.

The Cinque Terre is wonderful, but in July it's going to be like Disneyland on the trails. Unless you and your daughter are avid hikers who aren't going to mind crowds on the trails, personally I'd skip it or at least limit your time there. There is more to the Italian Riviera than the Cinque Terre, though in summer it will probably all be pretty busy.

Your trip looks to be well organized. The only suggestion I'd make is to fly from Nice to Paris Orly. 1 H 25min. Easyjet and Air France fly this route.

If you love Renaissance painting, sculpture and architecture, you'll want to stay in Florence and day trip to Siena. If not, you could spend all your nights in Siena and day trip to Florence to see the highlights. Unless you have a big preference for art or a major aversion to it, I think 2N in each is a good plan.

Expect the Cinque Terre and the French Riviera to be very crowded . . . and hence, not very enjoyable. Others here have suggested staying farther north/west (not exactly sure of the direction but toward the French border) in one of the other coastal Italian towns. You can get to the CT towns easily, yet avoid the masses of daytrippers. Why did you choose a week on the Mediterranean? The CT is good for hiking and is scenic, but the beaches are small and mostly pebbly. The French Riviera has much better beaches (though many are also pebbles rather than sand) and charming towns and villages to explore. OTOH, the crowds and high prices may make it less desirable.