One night in Naples

Unclear to me if there really is a "hydrofoil", but the ferry is a reliable product. You should download the official Fixed Price taxi sheet, because the drivers will try to charge you extras as a matter of course. I would use a taxi from the airport and a taxi called by your hotel, even if that's after you have checked out and left your luggage at the hotel for a walk-around the second midday. There will be lines for the better pizza.

https://www.napoliunplugged.com/tariffe_taxi_2017

We stayed here (2014), and I'd say it matches your needs. There are many other options. We valued the strong air conditioning. It is small-medium sized and personal feeling.

Hotel Palazzo Decumani, Via del Grande Archivio , 8 Napoli 80100
+39 081 4201379 - 4109144 palazzodecumani.com

Palazzo Alabardieri is near waterfront in Chiaia district, more upscale area, very quiet hotel as it is located down a side street. Palazzo Decumani was also highly recommended to us.
Why don’t you take the train to Sorrento? Or a ferry?

Thanks for the recs! We want to take a boat just for fun. We'll be on plenty of trains for the rest of our trip, but of course we're open to the train to Sorrento as well.

We liked the area of hotels on Via Partenope which has views of the sea and a pedestrian promenade. There are several waterfront cafes and pizza nearby. We stayed at Grand Hotel Santa Lucia across from Castel d'Ovo. That area is not too far from the ferry. Taking the hydrofoil is an excellent idea and I wish that we had done that from Naples to Sorrento. We had hired a driver, but the roads are curvy and mountainous and I got very car sick. Taking a taxi from the airport to your hotel and then from your hotel to the ferry would work well. There is a taxi rank on a side street right by Via Partenope.

Thank you! Santa Lucia looks beautiful with the sea views!