Fly into Rome April 5th 2020 afternoon out of Rome April 15th in the Am, Itinerary help

I think your last itinerary (Florence, Naples, Rome) looks better than the first one (Rome, Naples, Rome), but I would suggest you move a night from Naples to Florence. You're only allowing yourself one full day in Florence, and that would evidently include a side trip to Pisa, and 4.5 days in Naples seems like more time than you need to accomplish your wishlist for that area. All of your transportation between destination cities is best done by train. Flying between cities would actually take you much longer than traveling by train.

I completely agree with Frank. Definitely take a day away from Naples for Florence. The second option makes more sense.

Second option works a little better. Too many nights in Naples - cut at least two and add to Florence. Do Pisa as a half day trip (or a short day) from Florence. The principle catacombs are in Rome off of the Appian Way. Not familiar with catacombs in Naples. Capri would be a full day trip from Naples.

I think they're talking about these 2 primary catacombs in Napoli:

http://www.catacombedinapoli.it/en/places/catacombs-of-san-gennaro-naples
http://www.catacombedinapoli.it/en/places/catacombs-of-san-gaudioso-naples

But I would agree that the 2nd itinerary looks better. Capri will indeed take a full day to explore (I recommend skipping the Blue Grotto and hoofing it to other locations around the island.) It's very easy to do on your own - no tours needed at all - armed with some pre-research and a map from the tourist info office. This is is not a great day trip if it's raining, though, so flex your plan with the weather as needed.

https://www.capri.net

Definitely the second itinerary looks better, especially making use of the trains. As previously stated four days / three nights in Naples should be sufficient for what you want to see. One thing you consider the Naples National Archeological Museum, that is where the actual items from Pompeii are housed, it is worth it.

Have you bought the plane tix? You could save precious time by flying home from Naples or Florence. Did you consider Venice at all, instead of Naples? I question whether doing both Herc and Pomp justifies the same number of nights in ROME and naples. (Don't get me wrong, the Naples area is great. But it's an advanced topic in Italy.)