Gee I wish that I knew how to do that quote thingy.
Skoi, The Naples museum is really nice. It has awesome artifacts. If you would like to stay in the Naples area then that is a great choice. It is just that the actual city of Naples is not worth wasting your time. Also I will mention seeing the Caserta palace (you can google it). It has beautifully landscaped gardens. April would be a really great time to visit there. We went in July and it was soooo hot.
If you do not think that you are going to be in the Naples area again, then I would consider seeing Pompeii, the Amalfi coast (Sorrento area), or Capri. We will possibly visit Capri this trip because the last time we went there my DD got sick and we had to head back to Naples after 2 hours. If we had went there at the beginning of our trip, we would have stayed a few days. In all of my travels I think that Capri has the most breathtaking views that I have ever seen.
As far as driving goes, if you are driving on countryroads or highways that is a possibility, but I would NEVER, EVER drive in a major Italian city and I live in Europe. The train is a very easy and cheap form of transportation that takes you everywhere. If you want to go to Pompeii or Sorrento you can take the train. You can get a taxi from the port to the train station for around 20 euro (for the whole taxi, not per person). Make sure that you confirm the price with the driver before leaving. Boy, I could tell you some stories. You can get to Sorrento, Positano and Capri right from the port by hydrofoil. You can take the ferry also but the hydrofoil is much faster. It is around 17 euro to Capri and a little less to the Amalfi coast. (If you are prone to sea sickness make sure you take your meds).
I do not want to discourage anyone from their plans. I am just trying to give a little helpful info and a few options. Some of the excursions are so expensive and you can see the same things or more on your own for a fraction of the cost. If you have any tips or advice please make sure to share. Also we would consider sharing a tour with other cruisers depending on the port and the cost.