Lesser visited places in/near Rome

The Aqueduct Park is well outside the city center but easily reached by the Metro. It's definitely off the tourist path, and we had the place pretty much to ourselves. If you use a driver instead of the Metro, the Appian Way is a short distance away.

https://rome.us/ancient-rome/park-of-the-aqueducts.html

To me, it doesn't make sense to visit Siena and go to Rome the same day. We did our first visit to Tuscany (4 nights by rental car) from a cruise termination. Rented walking distance from Civitavecchia shuttle bus circle, stopped at Viterbo and Orvieto for evening arrival at our hotel outside Sinalunga. Siena is both too far, and too rich a destination to visit for only 3-5 hours, and the trip to Rome from there is tedious, even if you don't have to do the driving. Rush hour around Rome must be awful. I'm not denigrating Orvieto, a wonderful visit, but it's just not as rich a destination city as is Siena. (I'm not saying which is better, I'm talking about density of attractions and history.) We liked Viterbo, but it's not remotely as nice as Orvieto.

Having a car service is ideal for the two attractions in Tivoli, and unnecessary for Ostia Antica. However, I believe Ostia (haven't been there) pairs better with Civitavecchia. It should be pointed out that Orvieto is easily accessible from Rome by train. You imply, but don't explicitly say, that you want to take advantage of the car service; But maybe you enjoy the convenience, regardless of the destination. (Not judging, just talking about local travel options. And you don't say if physical limitations are involved or not.)

You haven't raised the issue, but if making the too ambitious trip of Pompeii as a daytrip, it's much better to take the Frecciarossa train and use a local car service if desired in Naples, but there's a perfectly good commuter train directly from Naples to Pompeii Scavi. I think with the Frecciarossa, this trip (which I am NOT recommending) could be faster than Siena by car.

I think your desire to visit the Coliseum a second time says something useful about your travel style, but I don't know what that insight is, exactly. I'm not saying no one needs to do something twice; I've been to the Roman Forum three times, but it used to be easier to get into the Coliseum. There is SO much to see in Rome and around it.

There is no "equivalence" between Hadrian's Villa and the Coliseum, but I think both are equally important and rewarding destinations, but Hadrian's takes more travel time and physical effort. It's actually a rush to do both Tivoli attractions in one day, but with a car service, it's entirely practical. Look up daylight hours for your visit.

https://community.ricksteves.com/travel-forum/italy/pompeii-day-trip-from-rome-2c38f926-9036-480d-95fd-403dd7694e4a

It's outside your 20-mile radius, but a spectacular site and doable: Pompeii. I was in Rome a month ago. My brother, who was in Germany on business, visited me in the Italian capital for 1.5 days. We decided to go to Pompeii for the full day.

It is fascinating to see the ancient Roman city destroyed in 79 A.D. by a volcano. And Mt. Vesuvius still looms menacingly over Pompeii. There is a fast train from Rome that gets you to Naples in 1 hour, 15 minutes. From there, City Sightseeing has a shuttle bus pickup point across from the Naples train station for the 20-minute trip to the Pompeii site. Rick's guidebook has the details.

If you want to spend a very long day in Naples, a tour of the Archeological Museum and a quick walk of the city are worth it, too. A restaurant in Naples claims to have invented the pizza. My brother and I wanted to have dinner there, but there was a line out the door and down the block.

Don't attempt to visit Siena as a day trip from Rome.

Consider Castel Gandolfo or Tivoli.

hey hey jon
have you reserved a private driver that day of arrival, gave them info what you want, how much you're comfortable paying, and are they willing? don't always go by times rome2rio or goggle tell you, you never know what the crazy traffic will be like, accidents which adds more time, the cruise port is about and hour+ to rome, the time it takes to get off the ship with i'm sure couple thousands all looking for a taxi, tram to station all trying to get to same place to see same things as everyone else. do book and confirm your private taxi transportation with email receipt. how far they can come close to port or how far you have to walk to meet them, hopefully with them holding your name. i've seen the ugly getting of the ship, they all in a hurry
the time it takes to get to siena and to spend only that short of time is not worth it to me as tim mentions. but this is your trip.
your days are short and it will be crowded since it's a busy time of year
getyourguide.com
colosseum rome. few tours to check out and if one interests you
withlocals.com/ rome
beautiful countryside day trip: castelli romani
get out of the hustle and bustle of rome, take the train to frascati, about 30 minutes. meet pierpaolo and take a journey visiting the pope's palace summer home, village of nemi and the lake with it's history and goddess diana of hunting, village of frascati, with family owned bakery/pizza oven with the "best" porchetta sandwich, and the bakery goodies that nonna rossana still baking at age 93. town known for white wine and it's vineyards. highest town of rocca di papa
lacucinamagazine.com/ famous buxom cookie of frascati ceralli.it the bakery/pizza oven
italymagazine.com/ lake nemi and it's wild berry
article old but gives you info about this area, just some reading up
then a ride back to train station and back to rome
don't forget to have gelato along the way
aloha

Thank all of you for your insights and suggestions. I know the Siena visit would be “tight: but I'm hoping I can work something out with the driver and maybe remain in Siena longer and get into Rome later in the evening. I realize Siena merits several days; our visit would be limited to the Piazza del Campo a walk to the Piazza del Duomo, visit the Duomo, and walk back to Piazza del Campo, hopefully having lunch along the way. We've been to Pompeii and Herculaneum on a previous trip, both sites and the tour guide we had were fabulous, even though we were there in August with blistering heat, literally hillside fires burning, and intermittent water shut-offs. We considered a day trip to Naples but thought it a bit much as we'd like to walk the streets, have a meal and visit the spectacular museum. As we're senior-seniors but fully ambulatory, the 2.7 km walk to and from the train station might be a bit much for us. Are taxi's readily available?

No one mentioned the Catacombs of Priscilla, I thought I ran across RS noting at some time in my travel readings of the past that this site is less visited than other underground/catacomb venues. Regarding the Appian Way, would it not be pretty crowded even in April?

We’ll take a closer look at Aqueduct Park, Nemi, Frascati, Castel Gandolfo, Orvieto and other places suggested; and, oh yes, several gelatos are in our plans.

On a slightly different track, if anyone that posted has a recommendation{s} for small and, again, off the beaten path, places to eat in Rome we would welcome them. We enjoy friendly staff that will help us with our limited Italian and delicious food, not a plush atmosphere or expensive linen table cloths.

Any eatery on the Piazza Navona is probably worth it in part because that square is so beautiful. Piazza Navona is in the center of Rome.

Catacombs of Priscilla - yes. We have not been to the Appian Way catacombs, but we spent a week in the Parioli district of Rome one year and went to Priscilla. We waited about 20 minutes for an English tour and no one else showed up, so we got a private tour! It was great. And you will then be close to Viale Parioli, where there are many restaurants to choose from, virtually none with American tourists.