If we only have time for one, should we do Pompeii or Herculaneum?
Since you mentioned bringing your cellphone with you (and I have no idea of your home location) do check to see what data, messages, and calls may run you if outside your home nation. It can get very spendy, very fast, especially on cruise ships where they generally charge all the market will bear for their private service.
If it was going to be more than 2 days only, I would have suggested checking if your phone is unlocked and request it be so if not. and using a local SIM.
Another option, if you’re not needing your primary phone as a camera, is to consider bringing an older spare cellphone if you have one. If it gets lost, damaged, or stolen, it’s often a whole lot less painful than losing a new one, especially if you happen to still be making payments on it.
Not a huge issue for a lot of people on this board who tend to not be addicted to $1000+ US smartphones, but worth mentioning.
And again, I cannot stress enough how badly some cruise lines will gouge you over any data/cellular use onboard.
https://www.cruisecritic.com/articles/what-to-expect-on-a-cruise-using-a-cell-phone
We used our Verizon global pass, $10/day and no problems. It’s perfect for this type of trip. I wouldn’t use it on the ship, but it’s fine in Rome.
Pompeii is well-excavated. I’m not sure the same is true for Herculaneum.
Many carriers do have pass features that will do the job.
The part of planning is to do it ahead, not after getting an unpleasant surprise on your bill! Or finding yourself separated from friends and family while abroad and finding your carrier doesn’t have an International program or partner.
And yeah, something like that is perfect for just a few days, again I’d have advised an unlocked phone and global/local SIM if it was more like a week.
The reason I want to be careful is especially if you want to share photos or a short video is the data will add up fast.
Text messages, minimal issue (in most areas), and people of the age of the board have the expectations that long-distance/international calls should be short from habit from the days when long distance calls were a thing.
But a short video, or a high-rez picture seems real innocuous as a MMS - until it isn’t.
Again, I don’t think our OP was at major risk, but if we’re planning ahead, it’s one more thing to check.
In general (this is carrier and plan specific) the Big carriers (Verizon, T-Mobile, AT&T) have reasonable international rates on most of their plans, although it may require a pass or additional surcharge for the service. Smaller companies, like Consumer Cellular… you may have more difficulties getting service and much higher rates.
Pompeii is iconic. Herculaneum is a wonderful sit. It’s where the affluent people lived. I’d say Pompeii if you only have time for one.
From my personal experience, I wish I had calibrated my expectations for Pompeii correctly. I thought it would be amazing, but I found it only fairly interesting; I think most of the actual antiquities and mosaics have been moved to the Naples Archaeological Museum
We made a trip to the Naples museum specifically because of all the originals from Pompeii that were there. It was worth it, but Naples was great in its own right. We liked Pompeii a lot; the experience was enhanced by the trip to Naples.
I was just in Italy this summer with my son, but we were in northern Italy.
A couple of notes.
Watch out for Italian trains. I’m used to Japan where trains run on time and that isn’t necessarily the case in Italy. The express trains are better, but even so, we had delays at times.
I used an eSIM Airalo and it’s dirt cheap. Because we were there for several weeks, I bought 20 GB for $33. They have cheaper deals such as 1 GB for $4.50 and valid for seven days. 2 Gb is only $8.00.
If your phone can take eSIMs, it’s really cheap.
I don’t suppose we could do both the same day and still catch the train back to Rome…
We always spring for the ship Wi-Fi and I imagine we’ll just use the AT&T day pass while in Rome since it’s just 2 days. Last year in Europe we used E-sims and it worked well but not worth it for this trip.
We didn’t do the museum and Pompeii the same day, but it would have been probably 9-10 hours to visit both and take the Circumvesuvia train to Pompeii and back.
I’m sure it’s possible, but I think it would be exhausting. There’s so much in Pompeii that it would be a shame to rush it. My wife was teaching ancient civilizations at the time, so seeing the originals that she had taught about was important. But the reproductions at Pompeii are quite good so you’re not missing too much.
We could have spent more time at Pompeii, but the Amalfi Coast was calling. 
That’s my answer too.
There’s nothing like seeing sleeping bodies frozen in time, and a pyroclastic explosion of lava.
I agree with this. I’m glad I went, but it didn’t blow me away.
ETA: No pun intended. 
Both sites are poignant and, for those of us in the Pacific Northwest, a reminder.
These are all wonderful pointers and I’m grateful to all of you for your responses!
Then you’re well prepared which is all I can ask! All it takes is one time handling that call where a customer is shrieking at your over $200 in increased cell fees for a one week cruise for one to become… sensitized… to that particular issue.
Oh, I have no doubt! Being in a “customer-facing” type of job myself I fully know how much humans suck 