Italy trip

Pontedera is the train station to go to from Rome (after you change trains in Florence) and then taxi to Borgo Alle Vigne You can book that part in advance using https://www.trainline.eu/
No need for passes; all train stations have either a computer self serve machine that sells tickets or a person there. Otherwise rent a car.

Borgo to Florence you just go back the way you came i.e taxi to Pontedera and then the train to Florence.
There are trains from Florence to Cinque Terre Milan and Venice.
It would make sense to go Florence to Venice to Milan to Cinque Terre in that order all possible on the train. Given everywhere you want to go I would say you need 3 weeks?

edit: Forget this suggestion if u were trying to go to all those places on daytrips from Borgo Alle Vigne

I'll venture a guess that you're staying at Hilton Grand Vacations Club at Borgo alle Vigne? It's an important detail as a car or private drivers may be mandatory for that location as there's no restaurant or market on site and none within walking distance. Just glancing at reviews, many posts mentioned having a car.

Venice and Milan are too far for day trips from this location but reviews list plenty of other smaller towns to see which are shorter distances away. Personally? If cities were your main focus, I would have chosen a different base, probably more than one, and on train lines as you don't want to mess with a car in the cities anyway. But you are probably trying to use points?

When staying at an isolated location, it's best to plan day-trips based on proximity.

Unless you fancy getting up very, very early (the Pontedera train station is 12 miles and at least 23 minutes from your lodgings), your best rail option to the Cinque Terre is a train departing from Pontedera at 9:18 AM. It reaches Monterosso (randomly-selected town) at 11:38 AM. The last train back with a connection to Pontedera leaves Monterosso at 5:07 PM. That is precious little time to enjoy the five Cinque Terre towns. They can be very busy, and you'll need to use the train to move between them. I think both walking and the boat would be too slow.

Venice is 3-1/2 hours from Pontedera, so not really a viable day-trip. It's a place where you need a lot more than half a day. Milan is about 3 hours away. I wouldn't do it unless you just have two goals: The Last Supper (must get tickets ahead of time; may already be too late) and the Duomo. Otherwise, Milan wouldn't be anywhere near the top of my Italian target list.

Look at places much closer to where you're staying: Lucca (75 min.), Siena (90 min.), maybe the coastal resort of Viareggio (50 min.). They can all be reached by train, but taking a taxi back and forth between your lodgings and Pontedera is going to be crazy expensive. Much as I hate to say it (I'm a big fan of public transportation), you're going to need a rental car, and if you have a rental car you may as well drive to your day-trip destinations. That will open up the possibility of seeing many small towns that have no train service, or at least no service to a conveniently-located station, like Volterra and San Gimignano.

Research the Italian driving rules very carefully. Many folks come to this forum 6 to 9 months after they return home, complaining about the very costly traffic tickets they are receiving.

• All drivers must have an international driving permit (from AAA) along with their US driver's license.
  
• Italy uses a lot of speed cameras. You do not get 10 mph of leeway. The fact that you do not see any enforcement vehicles does not mean that the speed limit is not enforced.
• Historic districts are often off-limits to vehicles or to non-local vehicles. Study signage in advance. If you drive into a ZTL, you will get a ticket. If you wander around, lost, you may get many tickets.
• There may also be bus lanes you're not allowed to drive in. Assume there is a camera taking a picture of your vehicle.