Pompei, Herculaneum or Paestum

Have you read descriptions of the three and felt any kind of attraction to any of them?
Pompeii is extraordinary and large. Herculaneum is smaller but has some elements that are more intact, making it appealing with limited time but I would choose Pompeii first for its significance. Paestum is more intact than any temples I saw in Greece, also quite extraordinary, but it is farther away and so unless you are "temple buffs," I'd still choose Pompeii, which has it all--whether you care about history or science. The view of Vesuvius you get from Pompeii is more compelling than I think climbing the volcano would be.

Where exactly will you be staying?

Pompeii and Paestum are both amazing sights, very worthwhile

We've done them all. Depends on what you want. Pompeii can be VERY HOT and CROWDED. We actually loved Herculaneum. We spent 4 nights in Sorrento and followed the RS Italy book to Herculaneum and did his tour walk thru - we LOVED it. If you choose this option, definitely follow his book and tour and don't miss the stairs at the end that take you down to where the skeleton remains are - so overwhelming. We also had some of the BEST Pizza we had in our 3 weeks in Italy at Pizza Luna - it's on the LEFT in the main town as you leave Herculaneum and head to the train station. They don't speak English, but it was super easy to order a Pizza and wine. We sat outside - still one of our favorite memories.

Thank you Valadelphia and Christine. I guess I should read more about both of them and see if anything resonates. Frankly, none of them really grill my cheese but I know it would be insane to be that close and not visit them.
We will be staying for a week in Praiano. For Napoli I suspect we will find a place in or closer to visit, so not expecting to go that far from Praiano.

Good points. Thanks Chinalake

My wife and I spent 4.5 days there, doing trips out of Salerno
You'll see my posts - about two years ago.

We spent most of our first day in Pompeii it was interesting. I had read a ton in advance, plus had printed out a guidebook and marked up a map.

When we went to Paestum, it was a breath of fresh air - in many ways. Here's a link to a YouTube video I did (I think I have 3 at YouTube). https://youtu.be/WbJdy9oWtwk

The train ride is long - 20 minutes from Salerno?
We missed the train to go there and had to take a bus - the trains don't run "constantly"

If I had a free half day, plus, I'd go there.

There's tons to do and see in Naples.
It's all an issue of prefetences

All are outdoors, so it's nothing like a museum experience (though I did find the museum at Paestum interesting). I mean, people were buried by hot ash 2000 years ago, and we're still talking about it--how is that not interesting?! (I kid, different strokes and etc. etc.)

Pompeii is well worth a visit! We spent the night in the town and about 3 hours at the archeological site the following morning. Being some of the first ones in gave us the place to ourselves for about 1.5 hours. Haven't visited the others.

https://community.ricksteves.com/travel-forum/italy/herculaneum-and-pompeii-questions

There actually more than 3 choices. I'm not urging you to give them as much consideration, but a multi-day ticket (only one admission to each site is included) offers not only Pompeii and Herculaneum, but also Boscoreale, Oplontis and Stabiae. Many, many posters here laud a separate attraction as a very easy day-trip from Rome, Ostia Antica. Because it's so much more work to visit, it doesn't belong in this discussion, but I should mention also, Hadrian’s Villa in Tivoli.

Your visit choice also depends on where you are sleeping. It is exquisitely HARD to visit any of them fast and cheaply from any town east of Sorrento. (Well, maybe Pompeii isn't so hard from Salerno. But it's not close to the train station from Salerno, while Pompeii is across the street from the train station used from Sorrento.)

Another, non academic/cultural/intellectual issue is that only Pompeii has full dining inside the site. (Is it OPEN during the pandemic????) It's not possible to see everything in Pompeii in one day, so many guests love the chance to sit down in an air-conditioned cafeteria and eat a full, hot meal. (Tickets do NOT permit you to exit and re-enter after going to a real restaurant.)

Visitors with mobility limitations may lean towards Herculaneum, but it's a fifteen-minute, steep downhill walk from the Circumvesuviana station. And the terrain inside the attraction is almost as uneven as in Pompeii.

Because it is an important UNESCO WHS, we planned to visit Paestum from Sorrento (five nights in Sorrento.) But it is just too far as a realistic daytrip from Sorrento. Also note sunrise and sunset in your visit month!

We've been to all. Each are amazing. We Iiked Herculaneum more than Pompeii as the ruins ate more it tact and not as destroyed by the volcano. Paestum was our favorite. The ruins are more preserved than most you would see in Greece.