Where should we go?

If you do not have tickets yet, do not fly into and out of the same city. See if you can fly into Pisa or Florence, rent a car and drive immediately to Montalcino. It is less than two hours by car so doable even after a long flight.

Assuming 7 nights, spend 3 nights in Montalcino and day trip to other Tuscan towns.

Drop your car in Orvieto, take the train to Rome and enjoy your last days (4 nights, I hope) there before flying out.

I'm not sure why you are worried about combining Rome and Florence, except that your time is pretty limiting. You could get off the plane in Rome and go directly by train to Florence (if you can't catch one of the few direct trains per day from Rome's Fiumicino airport to Florence, change in Rome to a Florence train), then come back to Rome for the end.

I've been to Italy a few times. I've been to Florence only once, and honestly, it wasn't my favorite city. I'm not a museum person. But it makes a practical base for day trips. I went to Siena and Pisa days with three nights in Florence itself. I don't regret visiting Florence at all, even though it wasn't my favorite. Places I enjoyed more are probably too far north to be practical with your short time in Italy.

Exploring the Tuscan countryside might be more to your liking - but you probably would want a car to do that, and I'm not sure driving immediately upon flying in (jetlagged) is a great idea, either. It would make more sense if you had more time. You could start in Rome then head north when you have gotten over the jetlag somewhat, but then you have to go back to Rome at the end...

You could also go south immediately to Naples or Sorrento and visit Pompeii or the Amalfi Coast, Capri, etc.

Why not stay in Rome, go to Orvieto for a night or two, return to Rome and fly home. There is plenty in Rome alone to keep you occupied for the week of you want to keep your trip simple. We spent 9 days in Rome because we got such a great airfare, couldn't pass it up. If you have a similar deal, grab it and enjoy.

There are literally thousands of options. Mull over if you want to rent a car or not, and how far you would like to travel from Rome (are flights booked?), then open up your guidebook and look at places.
There is no rule that you must see Florence or Venice on your first trip to Italy. It can be nice to contrast a bustling city like Rome with a smaller village. Once you determine if you will drive or not, the options should become clear (googling a train map can be extremely helpful in this regard too).

agree with Orvieto ...beautiful place and lots to see

You all make some great points! To answer a few questions:
-We will need to take public transportation as we don’t feel comfortable driving in Italy. We tried driving in a foreign country before and it was pretty hilarious (scary).
-Our flight is not yet booked. I figured leaving from the same place we came from would be most economical and we definitely want to see Rome.

I also had the idea of using Florence as a base to see other Tuscan towns but I read that didn’t make sense and is a waste of time. I guess it’s a little challenging trying to fit different towns into 1 week without rushing.

Most guidebooks have a "how to get there" section. Take a look to find somewhere accessible by train or bus. Orvieto is a nice suggestion several have made.
I often also just google "train map Italy" to see what's on the train line--you just might find something that way.
At least check open-jaw flights, as they can sometimes not cost considerably more.
I agree it makes sense to hold off on the Tuscan countryside for a longer trip and when you feel comfortable driving. Schlep your stuff onto trains and such while you are young.

I assumed your RT flight to/from Rome was already booked; if not, I might suggest flying into Venice out of Rome and take the trains in between.

I still say Florence for a few days is a good option, just because it's so easy to get there by train from Rome. The day trips I suggested are easy by train or bus. Siena is beautiful - I think I would have preferred staying there vs. Florence myself, but Siena to/from Rome may be a bit more complicated. Florence is easy. But I would go there first as soon as you get off the plane and come back to Rome and have all your time there - don't split it up. It might seem like a lot to try to take a train after a long international flight - but I would try, it will make better use of your limited time.

I have never driven in Italy - looks too dicey for me especially when some cities have ZTL (non-residents not allowed to drive in some cities). But I have found driving in other countries (Slovenia, Bosnia, Croatia, Czech Republic, France/Normandy) very easy and even fun. So on future trips, don't fear driving anywhere you go! Some places are easier to drive in than others.

Whether Florence makes sense as a base for seeing other Tuscan towns depends on which ones you want see and how you propose to get there. Yes, if you're going to rent a car for part of your trip, it wouldn't be a great idea to try see Tuscan hill towns from Florence. But if a place much less frenetic than Florence, though larger than a "town", is of interest, Lucca's lovely and easily accessible by train. There are one-day tours that would get you out into the countryside. I believe San Gimignano + Volterra is one possible combination. There are disadvantages to big-bus tours (not least being that they tend to go to a lot of the same places, leading to tourist crowds), but for seeing two or more small towns in one day, they can be very practical. Several folks on the forum have recommended Tours by Roberto, which has some tours you can join (registering in advance) as well as private tours. I have no idea of the cost, but I think they get you to less touristy places, and I believe the groups are small.

I found Orvieto lovely and recommend it as well. It's doable as a day-trip from Rome by train, or it's worth an overnight. It has quite a lot of sights, and the beautiful historic district on the hill is quite large and made for wandering. Orvieto gets a lot of tourists, many of them Italian. To the extent that many of the latter show up just for the day or a weekend, I think a mid-week visit would probably be a bit quieter. However, it's not hard to leave the other tourists behind by veering off the direct path between the top of the funicular and the cathedral.

Since you've not purchased airline tickets yet consider flying into Venice and back home from Rome. With your limited amount of time on the ground anything over two base cities will result in a lot of "lost" time getting from one place to another. My suggestion for Venice is because it is a truly unique city and a great place to get over the long flight from the U.S. Do some google searches on Venice and see what you think.

Since it sounds like you want to avoid a 2 city trip ; which I get I try to mix cities and scenery on our trips rather than all of just 1 or the other.
I really liked Florence and am not a museum person. The way it just has not changed in centuries, there is historical stuff all hundreds of yards away from each other and mostly outdoors in the elements and without barriers as such places would have if in the US plus the pedestrianized aspect of most of the streets in town were the main things I liked about it.
But you can always see Florence on your 2nd trip to Italy ; combine it with Venice and the Cinque Terre for a mix again.

For this trip ; why not train to Orvieto immediately when you fly in.
Stay there 1 night, rent a car in Orvieto drive to one of Montalcino, Pienza, Montepulciano stay in one of those small towns 2 nights ; drive back to Orvieto drop the car off and train back to Rome for the rest of your stay.

There would be close to zero ZTL fears in the driving I mentioned and the driving you would be doing would be super easy ; as easy as any state in the US.
That ticks all of your boxes, just have to get over that fear of driving in Italy. It is the cities that are problematic and can be scary to drive in, the country roads are the same as country roads here.

In Italy, they have a saying; Roma, non basta una vita - For Rome, one lifetime is not enough.

If you need a break from the city, check out Ostia Antica (closer than Pompeii) or a walk down the Appian Way.

Don't miss Florence, it is wonderful. Skipping Florence with its wonderful Renaissance history and art is like not seeing the elephant in the living room.

Also, you can visit the Tuscany countryside on tours from Florence.
https://www.tripadvisor.com/Attraction_Products-g187895-Florence_Tuscany.html

Concur with mreynolds, Rome-Orvieto-Montalcino-Pienza-Montepulciano.

The roads in this basic straight line path are very good. There's plenty to see in this area.

Nothing is more than 2 1/2 hrs from Rome.