Naples/Rome/Amalfi in 7 days?

Why not fly directly into Rome instead of flying Naples to Rome? Rome definitely needs more than two nights.
Then take train to Naples and continue to your chosen location such as Amalfi.

Flights to and from Naples are significantly less expensive than Rome for some reason. Maybe Jubilee? But the idea is to take the train to and from Naples/Rome.

That's a whirlwind of a week to squeeze everything in. Personally, I've given up on trying to find "knowledgeable" travel agents. Doing it yourself isn't as daunting as you may think. I would highly recommend the Rick Steve's travel books which are loaded with practical information. You're especially going to need it on the Amalfi Coast. We spent 2 weeks there in Spring of 2023. Since Pompeii is part of your itinerary I'd suggest staying in Sorrento, however it's getting late in the year to be booking anything in that region. At least you've got a healthy budget. You can find some nicer looking hotels in Sorrento with ocean views. If your interested here's my Trip Report.

https://community.ricksteves.com/travel-forum/trip-reports/trip-report-2-weeks-of-day-trips-from-sorrento

As for Rome, I'd recommend a Colosseum tour that includes the Forum and Palatine Hill. We found those 2 areas far more interesting than the Colosseum. We used https://www.througheternity.com/ for tours of those sites and the Vatican on consecutive days.

Why not look at Ischia for some beach time and save Amalfi for another trip?

Look for "multi-city" flights- not 1 way flights- Fly in to Rome, out of Naples.
Compare the cost difference with 4 RT train tickets to/from Naples and Rome plus any other transportation costs- taxi etc to /from stations, and it may not be that much of a difference.
You are wasting time by flying in to Naples.
You will need to be IN your departure city night before departure (or Sorrento is OK if your flight is past noon but figure out your transportation now- I'd get a driver)

I would fly into Rome- spend no less than 3 nights
Train to Naples then on to Sorrento- spend remainder there- (or all but the last night in Naples).
Pompeii is easer to visit from Sorrento or Naples not so easy from an AC town.

Trying to get from Rome all the way to a town ON the AC will take most of a day. You don't have time to waste like that.

I would agree that Rome could use another night. Rome is so much more than just the Colosseum and the Vatican. And dont discount the effect of crowds on how long it takes you to see everything. Since your trip is only 3 months out, you may find advance tickets already gone, so may need to look at tours for the major sites in Rome that require pre-booking.

Strictly for practicality, I would agree that Sorrento would be a good choice to stay after Rome. Transportation along the AC is hugely problematic, especially in high season, and Sorrento, although technically on the Bay of Naples, and not on the AC, is a transportation hub. There is easy (although not comfortable) access to Naples and Pompeii via the Circumvesuviana train. There are buses to the major AC towns (although too few in number to meet demand). And there are ferries to Naples, Capri, and some of the AC towns. Do NOT be tempted to rent a car here in summer. There are umpteenth dozen previous threads about traffic on the AC.

You could really benefit from a good guidebook, like Rick's Italy book; especially if this is your first visit to Italy. Have a great time.

Thank you all for the feedback. Exactly what I’m looking for. It seems that Amalfi Coast and Rome might be too much in 7 days during peak season.

Would Rome-Ischia be more reasonable? I’ve never heard of Ischia before someone mentioned it here, but it looks beautiful. Is Ischia a good place for rest and relaxation?

Ischia is an easy ferry ride from Napoli and has beautiful beaches, some with volcanic hot springs. I find it lovely.

Ischia is certainly an option. But you will have to be in Naples the night before your flight. I would suggest you do 2 nights in Ischia and 2 in Naples so that you could still visit Pompeii and perhaps the Archeological museum

Personally, I’d just cut Rome from this itinerary. That’s what is making this difficult. You just end up short changing both destinations. There’s nothing wrong with just focusing on Naples and the Amalfi Coast. As I’m sure you’re finding, there’s no shortage of sights to keep you occupied for the week. Rome will always be there, it’s the eternal city after all.

I recommend staying a couple nights in either Naples or Sorrento to see sights on the Bay of Naples, then some nights on the Amalfi Coast itself. If you’re traveling in June 2025 things may be booked already. Salerno makes a good base here too, and some folks prefer it.

My suggestion is to spend one week in Rome! It's a magnificent city with so much to see and do. The only problem is that this is the Jubilee year so Rome will be even more crowded than usual. And more expensive.

So you could eliminate Rome from your itinerary and spend the week in Naples and the Amalfi Coast.

I posted a suggestion on your Switzerland thread. It will help with planning if you post your whole proposed itinerary. Is it only Italy? Only Switzerland? Both? More countries? The more information you provide in one post, the better we can help.