Pompeii + Archaeological Museum in 1 Day From Rome?

Yes— it can be done! Pompeii opens at 9am and it’s best to arrive by opening time so you start touring the site before it gets crowded and before the heat of afternoon arrives. The fastest trains from Rome Termini reach Naples in 1:15. Italotreno, the private train company in Italy, has a high-speed train departing Rome Termini about 6am and reaching Naples about 7:15am. There’s also an Intercity train leaving Rome Termini at 6:26 arriving into Napoli Centrale train station at 8:29am. After arriving at Napoli Centrale train station you transfer to the Circumvesuviana commuter train by going downstairs to what is called the Garibaldi station. The Circumvesuviana. ( “around Vesuvius”) train takes 27 minutes to reach the “Pompeii Scavi-Villa dei Misteri” station where one of the entrances to the Archaeological Park is located. ( BTW, don’t miss going inside the Villa of the Mysteries located here—it was the house of a wealthy Roman and has incredibly well-preserved frescoes on the walls and floor mosaics).
Plan on 3-4 hours visiting the massive archaeological site at Pompeii. There is a cafe on-site but it’s still a good idea to bring snacks. Also be sure to bring a hat, sunglasses, sunscreen ( there are no trees and therefore no shade) and your water bottle.
It’s 27 minutes back to Naples on the Circumvesuviana commuter train. Fortunately, the National Archaeological Museum of Naples, which displays most of Pompeii’s artifacts, is just 1.3 miles from the train station. From the Garibaldi station, take Metro Line #1 to the “Museo” Metro station. Most visitors to the National Archaeological Museum spend 2-3 hours.

You can check train schedules and fares for Rome to Naples trains at www.TheTrainline.com
Have a great Trip!
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The "fast food" place inside of Pompeii gets really crowded and there was quite a line when I was there spring, 2023. There's plenty of food sold outside the gates, so I'd buy a panini there and get extra water.
In my experience, the Circumvesuviana starts running late as the day goes on, and we found SRO. There is only a single track thru the tunnels, and trains get backed up waiting for their turn through. That was very frustrating after being on our feet for hours at Pompeii. Transportation in this area is not fast nor efficient, nor very organized, so planning an adventure based on everything running on time can result in frustration.
We were talking to folks on the Circumvesuviana who got on at Naples , had been on the train two hours, and still weren't in Sorrento yet.
I think the high speed train is only on certain Sundays, maybe, and is very limited availability.
A private driver from Naples to Pompeii would probably run about 100euros.
Pompeii is a glorious experience , and I wish you a great trip, once the realities on the ground are taken into account.
Safe travels!

In addition to the “Circumvesuviana” commuter train there is the “Campania Express” train which runs 4 times daily out to Pompeii from Naples. It uses the same tracks as the Circumvesuviana trains.
If you arrive in Naples by 8am, though, the Circumvesuviana should be fine.
There are Trenitalia and Italotreno high-speed trains running between Rome and Naples every day of the week.
I agree with Pat that it is a glorious experience to be able to see a virtually intact city from 2,000 years ago.

Just a couple of additions to the helpful info above....

The MAAN is closed on Tuesdays so pick a different day for this adventure. :O)

Pompeii scavi closes at 5:00 PM with last entrance at 3:30 PM in March, when I believe you'll be traveling. MAAN closes at 7:30 PM; they start clearing galleries at 7:00. Last "fast" train (Trenitalia) from Napoli Centrale to Rome departs at 8:30 PM so you shouldn't have to rush to catch it; grab a to-go supper at the station to eat on the train.

Villa of the Mysteries (Villa dei Misteri) is definitely worth seeing! It's not close to the Porta Marina entrance (the main entrance closest to the “Pompeii Scavi-Villa dei Misteri” Circumvesuviana station) but a good 15 - 20 minute walk from that entrance after you've entered the park. This is great map/brochure for reference; download it before you go:

https://pompeiisites.org/wp-content/uploads/Pompeiweb2023.pdf

Porta Marina is on the lower left of the map: Villa dei Misteri is the isolated site (#19 of Regio VI) all the way over on the upper far left on the map.

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

Did you have the faster Frecciarossa train in college? Month of year? Pompeii hours can vary with the number of daylight hours. It can be punishingly hot and sunny. I find the amount of travel too much for a daytrip at all, so I would not add the museum. If you do go, don't overlook the Farnese Marbles.

It seems to me that it's impossible to predict whether a taxi or the Circumvesuviana will be faster. Infrastructure is unpredictable in Campania. I lean towards the Circumvesuviana.

It can be punishingly hot and sunny

But probably not hot in March. Unless Susan is taking two different trips, prior posts indicate that's when she's going.

Yes, it can be done, more power to you, if you want to make it an 'All Pompeii Day'. Actually, the ruins, then the Archeological Museum are nice bookends with so many of the ruins' relics being at the museum itself. And yes, Tim, the Farnese Marbles are spectacular!

Some cautionary words. It's a l-o-n-g day--Termini back to Termini will be 10-12 hours, to be done right. So wear the right shoes, get a good night's sleep. And watch out for what I call sensory overload. In 2017, we did St. Peter's in Rome, on our own. Had Skip-The-Line tickets and they gave us some crappy earbuds that are supposed to describe what we were seeing, that rarely worked. We were going to make a day of St. Peter's, and we almost did. But...after about 5 hours of trying to absorb everything...and I knew it would be years until I returned (we're going again next April)...I had to get out of there. Too much opulence, too much everything. Point is...I think 3 hours at the ruins and 2 hours at the Museum should suffice.

Finally...where are you going to eat? If you can swing it, after seeing the museum in Naples you should be within walking distance to any number of great restaurants, although if memory serves I didn't see much on the other side of the street where the museum stands. Easy to look up. Also...when we visited the ruins, even though they have a snack bar, we had brought a couple of panini's, chips and waters (bring water on your own regardless) even though I don't think you're supposed to bring your own food in. But I think that's because they--rightly so--assume visitors are going to litter. We sat just inside the Porta Marina entrance, next to the Anfiteatro, and for 15 minutes ate our lunch in the quiet. It was wonderful, and we picked up after ourselves, not leaving a trace that we had been there.

Would it fit into your itinerary to stay a night? Even if you kept your Rome hotel and double-dipped, that would guarantee you could do both, with a bonus of getting a bit of Naples in the bargain.
I spent all day at Pompeii (which has gotten bigger since I was there last), so I can't imagine really feeling up for the museum, but you'll have time to rest on the train back I suppose!

EDIT- to my post.
I was referring to the newer high speed train from Rome to Pompeii. I believe it's only on selective days. Sorry I wasn't clear.