Advice on planning our first trip to Italy

Your plan sounds fine. I assume you are flying out of Rome to your home as well.

You can day trip Siena if you ahve a villa/agritourismo in the vicinity. And it isn't a bad vicinity. San Gimignano is a good location as are the towns of Montepulciano and Pienza. If you stay in Florence you can easily drop the car and train back to Rome for departure. Or, drive back and dump the car in Rome.

You will be missing Milan, Venice, Naples (unless you go there from Amalfi).

Do you fly home from Rome, or...?

Personally I'd take the train rather than renting a car, but your preference may vary, especially if you're set on an agriturismo (although some agriturismo hosts are certainly willing to arrange a car or van to transport guests from the nearest public transport station). You could take the fast train to Florence, stay there a couple of nights, and then use the local train to go to Arezzo. After Arezzo, return to Rome the night before your flight.

Train is the way to go for 5 days - getting out of Rome with a car can be very unnerving. Suggest fast train to Florence 3 days - bus to San Gimignano for a day trip and bus Siena for a day. If you can fly out of any other city than Rome I would suggest 3 days in Florence - fast train to Venice for 2 days and fly out of there. Venice IMHO is so unique it is hard to describe.
Another suggestion is to buy RS book on Italy as it will cover a lot of these places and you can choose which to see. Enjoy

Great advice, sounds like the train is the way to go. We have not booked our ticket home and could fly out of Florence or take the train back to Rome to fly home. Looks like we would take the train to Florence on a Sunday, would need to fly home Friday. Would love suggestions on where to stay, we would prefer air bnb's or VRBO vs big hotels. Also suggestions on Agritiurismo's to stay as well? Perhaps we won't need to rent a car at all or only rent it for a couple of days.

We will see Naples while in Almafi, we are also doing a day trip to Capri. We are with seasoned travelers during that half of the trip. The second half we will be on our own and pretty wide open. I do have the RS book, so much to see! Thanks for your suggestions.

We made a few mistakes on our first trip. The biggest was making assumptions... in other words, don't assume anything. We assumed we would be able to easily find the rental car office in La Spezia to return our car. (this was before US cell phones worked in Italy). We had to leave it in a parking lot after several hours of asking directions, and me failing to understand the answers, and attempting to find the place. We had to leave it in a parking lot over the weekend and go back Monday, when I spent more time driving around. (construction had blocked/changed the roads through town). It was a nightmare.

I will NEVER drive a car in Rome again... it was absolutely harrowing. I might consider renting a car in Italy, but only if I could pick up and drop off from a small town and limit the driving to sparsely populated areas.

Second mistake was trying to do/see too much. We had been to Sorrento, Orvieto, back to Rome to get the car, drove through San Gimaniano and on to LaSpezia to return it. By the time we got to Vernazza, our nerves were shot and we cancelled Florence (and had to pay for the room there) to stay an extra 2 days in the Cinque Terre. It was definitely the right move. (Even though Vernazza is very crowded now, we spent 5 days there on our last trip and loved every minute of it.) We try to stay at least 2 nights at each place we go in Italy now, often it's longer. Getting from place to place is pretty stressful, but we love travelling by train in Italy.

Try to learn a few phrases in Italian, it's not usually necessary but I believe folks appreciate it if we at least try. We also try to dress as much like locals as we can. Google Earth some of the places that you're going and take some "street view tours," it's fun and will give you a teeny idea of how things are laid out. Generally speaking, the smaller a town is, the better I like it, with the exception of Venice... no traffic, great exploring by foot. Now that we've seen it, we don't care so much for Rome, but we LOVE the Cinque Terre, Orvieto and the hill towns, Sorrento and the Amalfi Coast, Venice and its islands. Good Luck!

Milan is an option for non-stop flights back to the US.

I think we are leaning towards leaving Rome on Friday and taking a train into Tuscany. We will need to head back to the states the following Friday which gives us a full week to explore Tuscany. Can we rent a car in a smaller city in Tuscany to have for the week, to avoid driving in Rome? Return the car on Thursday and take the train back to Rome, flying our of Rome on Friday morning? I think we will save Florence and Venice for another trip to Italy. I like the idea of being able to take some time and enjoy Tuscany before heading back home.

My advise: Don't try and do/see too much.
2 weeks is not enough time to cover everywhere obviously and your plan while not bad: Amalfi Coast, Rome, Tuscany, Florence or Siena is about maxed as is.

The summer heat will slow you down as well.
I have more of an issue with the timing your seasoned traveler friends have proposed than your own plans.

Better to state nights than days (puts everyone on the same page).
4 nights is kind of bare minimum for Amalfi Coast. Since you are flying into Rome and I assume reaching Amalfi Coast the same day your first day/night is shot.
I assume you want to do a day in Capri and probably want to see Pompeii so I can see this being too short a stay for the region, especially since this area is where the summer crowds are the biggest factor.

After that 3 nights in Rome seems to me at least 1 night short as well.

I would not want to drive in Rome or very close to it, while driving in Tuscany is a breeze at least until you approach Florence where it becomes messy again (for reasons of laws even more than traffic).
Plenty of research to be done if you decide to go the car route. Car can be better in many cases for some areas but takes more planning for sure.

I am not saying this is true in your case but I think many who at first think small Agriturismo would be better off staying in one of the small walled towns in Tuscany instead ; like Montepulciano or Pienza.

You usually get better views, still has all of the charm and actually have things you can walk to not stuck on a farm dependent on your car for anything.

If you do Florence on this trip you have to save 3 nights for that, Siena could be done easily with a 2 night stay, so if you are going to do a smaller town first maybe end in Siena. However getting back to Rome airport from Siena will be difficult so Florence is better for that.
In general your plan of flying into and out of Rome when you are not starting or ending there is making things difficult.
Flying into Naples and out of say Florence would logistically save you time and effort.
Assuming you stick with Rome, you could train to Orvieto easily from Rome, easy to rent a car there and return it there when you are done touring Tuscany. Taking train from Orvieto to Rome Airport at end.

Can we rent a car in a smaller city in Tuscany to have for the week, to avoid driving in Rome? Return the car on Thursday and take the train back to Rome, flying our of Rome on Friday morning?

Yes. Try Orvieto. Easy to get to by train and the car rentals are near the station. You could go there in the morning (1 hour by train), look around, have lunch, rent your car and be on your way. Ditto for return. Or return in Firenze at the airport.