Sorrento to naples archaelogical museum to rome transportation

Are you open to a car service? It is more expensive, but it will be direct. I am going in September and using Positano Tony Taxi
https://www.positanotonytaxi.com/sito2/ to get from Naples train station to Pompeii ( where driver will wait w/ our luggage) then on to Sorrento. Marco has been very responsive via email with coordinating details. He even arranged a tour guide for Pompei.

The fast way will be the 35-minute ferry called “NLG Jet” which leaves Sorrento at 7:20am and arrives at Naples’ Port at 7:55am. The Circumvesuviana train takes from 1:15.

From the port, the Naples Archeological Museum is less than a four-mile €15 to €20 taxi ride.

The museum has lockers for storage, but oversized luggage will need to be stored at a luggage storage facility such as the adjacent “Bounce” Luggage Storage location.

www.Ferryhopper.com has ferry schedules and fares.

You can take the circumvesiviana train from Sorrento to Naples, and then the metro to the museum. We spent the whole day at the museum, depends on your interests, of course, glad to see you plan an early start. After the museum, you'd go back to the same train station, Naples Centrale, for your fast train.

You didn't ask, but I know the archaeological museum has lockers, not sure if they are big enough for luggage, but I think its likely. You could email them.

I emailed the museum and told them that we would each have a carryon size bag (and gave them dimensions) plus a backpack and they answered that they had luggage storage.

We are pretty frugal so private car is probably out.

Is there Uber or Lyft in naples, rome? Ive been told there are none in florence.

There is no Lyft. Uber in Naples and Rome just links you to licensed taxis and not independent Uber drivers. The result is that there is little—if any—savings for customers. There are reports that using Uber in Rome and Naples actually makes it more expensive than if you just use a licensed taxi to begin with.