Driving through Cinque Terre and Tuscany

Normally it is not recommended to drive to the Cinque Terre however as a parent who has traveled with a young child I understand the added benefits that come with having your own car given your extra needs.
I would rent the car from the Pisa airport.
The drive from their to either Riomaggiore or Manarola is simple. I have driven to Manarola and as long as arriving early or late (not midday) the main paid parking lot in Manarola is easy to find and should have available spots.
It is not cheap to park there but was convenient and looked safe to me.
Many complain about the drive but I suspect it is after Manarola as until Manarola the drive was simple, most pain part was driving through the town of La Spieza itself.

Driving in Tuscany is easy, you have to research in advance the unique aspects of Italian driving and laws (ZTL zones, need an International Driver License (go to your local AAA office and pay about $20 for this))
Your stopovers seem fine, looks like you are bypassing Florence which is where you would have the most ZTL concerns, possible bus lane concerns and more traffic.
The other towns you list are all fine to drive to BUT you have to find parking outside of town, because of ZTL and other restricted driving areas in general you cannot drive right into a town like you do in the US. So you park outside of town in a paid or sometimes free lot and then walk into town.
With a 1.5 year old, this is going to add time to your day, so keep your expectations of how many stops you can make manageable. You will appreciate how nice a town can be when it is car free and come back home and be disappointed your home town does not have a similar area.

Expect to be treated very well when you with your infant, Italians adore babies and young children and more understanding if they are crying, loud, then typical Americans would be.

The driving is easy, the roads are rarely straight though so either rent a GPS, bring a GPS or make sure you have a data plan or way to use your phone for GPS for driving at all times. I used the WAZE app on my phone and it was perfect for all the areas you are driving.
Dropping off the car before you reach the center area of Rome is a good plan, again need to avoid where any ZTL's start so have to research this for Rome but also each area you may drive to or through.
ZTL fines are very expensive so don't ignore that aspect.
Also there are constant speed traps on back roads entering towns and all along the highways and even an average speed monitoring system on the highways in Tuscany so be mindful of your speed at all times.
Your GPS app may alert you as you are approaching these (Waze does which was a nice benefit)

Tolls are pricey and may not accept your credit card so have cash for tolls and gas.
At gas stations if during normal business hours you can use a US credit card but during multi-hour lunch times and after hours (many are closed at night and Sundays) ; the pumps will work but not with your US credit card so you need cash and will not be able to get change if you overpay in cash.
Lunch times can be from 12-3 PM that they are unmanned though usually not quite that long.
Not a big deal, but helpful to know in advance. Cost me sometime figuring that out since I went unaware of this.

Since you are traveling with a toddler, it's probably easier if you rent a car at the PSA airport when you arrive. The Cinque Terre should be your first destination after your arrival, since later you will be farther once you visit the core of Tuscany. The drive from Pisa to the Cinque Terre is approximately 1.5 hours. I recommend Levanto or Monterosso as it is more car friendly and easier to reach than Riomaggiore, although farther (for Riomaggiore you have to go through La Spezia surface street traffic, and some narrow stretch near Riomaggiore.

The drive to Levanto or Monterosso is mostly freeway, until you reach the Levanto exit on the A12 to Genova (Genoa). Once you exit the freeway follow directions to Levanto. Then to Cinque Terre Monterosso once in Levanto. Whether you feel like driving there upon landing while jet lagged, or the next day after resting is up to you, depending also on what time you land. Levanto is not technically part of the Cinque Terre, but only 3 min by train from Monterosso. Levanto and Monterosso are easier to reach, both have plenty of parking, and a more proper beach, sort of sandy, for kids (aside from Levanto and in part Monterosso, the rest of the Cinque Terre, is mostly cliffs and very deep waters which are IMO dangerous for toddlers).

Once done with the CT, proceed back to Tuscany for the rest of your plan.

I am making some assumptions here, but please consider if you will have had enough sleep to drive--but at 1.5 hours (Pisa to Manarola), I have to admit that is within the "safe zone" my husband and I determined for our recent trip. However, we did not have to attend to a toddler on an overnight flight.
You might want to play it by ear--Cinque Terre is darn near pointless in bad weather, and rain can be common in October. I don't see the point if you are not hiking, but that's just me. There are some gobsmackingly gorgeous sand beaches (as well as rocky coastline without gazillion others) in southern Tuscany--so you could leave your options open.
We only drove around Pitigliano, but other than some trucks on the narrow coastal highway lanes, and some curvy roads in the interior, we found the driving quite easy.
Here is the gorgeous apartment where we stayed in Pitigliano. Lots of stairs, but oh the view!
https://www.airbnb.com/rooms/10797877?location=Pitigliano%2C%20Italy&s=bH9nfppQ

A few points to be aware of when driving in Italy.....

It's important to note that for driving in Italy, each driver listed on the rental form must have the compulsory International Driver's Permit, which is used in conjunction with your home D.L. (so you must carry both). These are valid for one year, and easily obtained at any CAA/AAA office (two Passport-sized photos required, which may be provided by the issuing office).

You may never be asked for an IDP, but failure to produce one if requested can result in fines on the spot!

You may also want to have a look at some of the posts on the forum concerning the dreaded Zona Traffico Limitato (limited traffic) areas that are becoming increasingly prevalent in many Italian towns & cities (especially Florence!). Some of these are enforced by automated cameras and some by local police. Each pass through one of the automated Cameras will result in a €100+ ticket and visitors often don’t know of these violations until several months after they’ve returned home. In addition to the actual fines, renters will also be charged by the rental agencies for providing information to the authorities. You may find this website helpful - http://www.slowtrav.com/italy/driving/traffic_cameras_speeding.htm

There’s also the possibility of fines for driving in bus lanes, parking tickets, tolls and speed cameras including the devious Traffic Tutor system which not only monitors instantaneous speeds but also average between two points. Violate either or both parameter and expensive tickets will follow!

A GPS along with a good Map is also prudent. Be sure to give some thought to the question of CDW and theft insurance. In Italy, buying CDW from the rental firm is usually compulsory, so coverage provided by credit cards will not apply. Check the Car Rental guide at http://www.gemut.com/ for more information. Their free "Car Rental" PDF Guide can be downloaded. You may also want to check the “Travel & Transportation” pages at https://travel.state.gov/content/passports/en/country/italy.html for other tips (look under "Travel & Transportation"). There’s also this website - https://it.usembassy.gov/u-s-citizen-services/local-resources-of-u-s-citizens/transportation-driving/?_ga=1.21563186.86862954.1474991758

Happy motoring!

Thanks all! Sorry for the delayed response but these suggestions have been very helpful.

I read somewhere that to enter CT one requires a ticket that has to be bought in advance online. Is that really the case and is it for a limited portion of the area? Also if we do decide to take the train to CT, what would be a good city to pick up a rental car for the rest of our trip from? Thanks again.

No, you don't need a ticket to enter the CT.

Driving from village to village would not be my first choice. Taking the train between villages is probably easier.

You might want to read this article on driving in the CT:

https://www.cinqueterreriviera.com/where-to-park-cinque-terre-world-how-to-get-there/

As I mentioned driving to Monterosso (the largest of the villages, and the most car friendly) or nearby Levanto, is easy and parking is available. If you drive there, I suggest you base yourself in the village where you decide to park. Both Monterosso and Levanto have a sand beach that would be more appropriate for toddlers.
The closest town with car rental offices is La Spezia.

You did say "a week," as in one week, didn't you? In my opinion, you have far too many destinations, even if you weren't needing to consider how a toddler will impact your activity. Yours is the second posting I read this morning which mentions Civita. I have to say, as I have done in many prior responses, that I am baffled by the hype, induced by RS, for this little boring hamlet. It's tiny, with nothing of interest, and quite cumbersome to get to. My advice is to scratch it.
Siena is pretty large, with much to see. Both it and Orvieto are each worth whole day, if not longer, visits. Staying in it with a car might be problematic, but being nearby makes a lot of sense. It will be easy to access Pienza and Pitigliano from there, or you can visit the latter from Orvieto.
When we last visited Pitigliano, a couple of years ago, we were able to park for free, a couple of blocks outside the historic center. The walk in is flat. There was also some paid parking just inside the walls. The main part of the center is also pretty flat; however, there is a steep decline towards the end of the main street.

Rosalyn:

About Civita I couldn't agree more.

The funny thing is that if 20-30 years ago you had asked an Italian where Civita was, 100% of the Italians interviewed (except for maybe some of those living in the Lazio region) would have had no idea where and what it was. I heard it on one of RS' books the first time when I moved to the US. Many Italians outside of that region, still don't know and have never heard of it.

Same with Castelrotto. I have virtually no friend or acquaintance in Tuscany who has ever heard of Castelrotto. Only some of my most avid skier friends who go often to Alto Adige, have.

Orvieto, Siena, and San Gimignano, have always been super famous. In part also Pienza has been famous for a long time (certainly in Tuscany), even much more so than Montepulciano, at least during the century BR (Before Rick).

You are planning to do WAY to much in the time allotted. You say you've got a week and plan to spend a couple of those days in Rome?
I suggest you pick up the car in Pisa, spend a couple of hours seeing the basilica and tower, then head for Lucca. Spend a couple of days there. Then head down to either San Gimignano or Volterra. Spend a couple of days there, with an afternoon side trip to the town where you don't stay. Then, take a leisurely drive to Rome through Tuscany for most of a day. Spend the rest of the time in Rome. When do you arrive and when do you fly out? If it's Sunday-Sunday, even what I suggest would be tight.

Be aware that Ken trots out his horror stories any time someone mentions driving in Italy. It's not nearly as scary as he makes it out to be, and anyone with a little common sense and preparation will have no problem avoiding ZTL's and speeding tickets.

We were planning on staying in Montepulciano for 4 nights and driving to some of the hill towns mentioned above. Would others recommend a better town to hang other than Montepulciano? We were hoping to do some wine tasting, eating great meals, and watching the people and lifestyle, more than a lot of hiking around. We're also in our 60's so now I'm wondering about all the up and down. Before then, we will have stayed in Rome for a few days, then driving to Montepulciano, then dropping off the car in Florence and taking the train to Monterosso, where we will stay another 4 nights. And then finally a train ride back to Florence to hang for 3 nights, and then flying home from Rome. Any thoughts or suggestions on how to make this even better?

Thanks, Kathy