First Italy Trip: Where should I put my extra day??

It depends on your arrival time and how grueling your journey is, and it is not a big problem to have two stays in Rome, but what a lot of us do is continue on arrival to one of the other destinations that is an easy train ride (like Naples) and put all of the Rome time together at the end.
As for the extra day, make a detailed list of what you want to do and see in each place and look where it would help--there is no rule that you have to put it where there is more to see or whatever.

ETA Which month? That can make a difference, for weather or specific events.

I think your schedule looks good. You're doing Rome, Florence, (Orvieto), Naples for a first trip versus the usual F, R, Venice but that's fine.

I would add an extra day in Florence since you're using one day for a day trip and either spend more time in Florence or add a day trip to Siena.
If you really like ruins you could consider adding a day to Naples and looking into Paestum, but only if Greek/Roman ruins are a highlight for you. If none of this interests you Rome will always swallow another day given everything there.

Have a great trip!
=Tod

what a lot of us do is continue on arrival to one of the other destinations that is an easy train ride (like Naples) and put all of the Rome time together at the end.

As valadelphia says, but I think it's a pretty worthwhile idea.

I'd also say you can't have too much time in Rome, so adding a sixth night there (all six nights at the end) wouldn't be a bad idea.

Alternatively, you could do an overnight in Lucca. It's worth more than a quick stop, especially if you want to see Pisa also.

Oops, forgot to say: The best sfogliatelle in the world is 5 minutes from the Naples train station. Antico Forno delle Sfogliatelle Calde Fratelli Attanasio Vico at Ferrovia 1/2/3/4. Walk over, show up, grab a number right away and wait your turn.

So worth it.

Enjoy Naples,
=Tod

I was going to suggest what hired man recommended. Except I was going to suggest a day trip to Capri if you added a day to Naples.

If you must fly RT to Rome then I agree with moving onward on arrival so you eliminate the split stay/1 nighter in Rome at end. Put all Rome nights at end of trip.

Do check on flying into Rome, out of Naples as well.

I wouldn’t recommend starting a first trip in Naples.
Orvieto is less than a 2 hr train ride from Termini and makes a great place to get over jet lag.
From Orvieto train to Florence, then down to Naples then back up to end in Rome
Give the extra day to Naples since it’s a longer travel day.

Orvieto 2 nights
Florence 4 nights- day trip Lucca/Pisa, Siena?
Naples 4 nights- day trip Pompeii, Capri or Paestum or AC
Rome 5 nights

If you do want to add day trip to Siena (very worthwhile) then you could give Florence 5 nights and Rome 4 nights.

Agreed with others, you should go far away from your departure city right away and then come and end in Rome, meaning you have even MORE time there! A plethora of extra days! (as each day you move you lose at LEAST a half day and definitely any major sightseeing time)

I like Christine's suggestions too for your extra days :)

Just the mention of Sfogliatelle has me dreaming of a return trip to Naples!

UPDATE

I will be going mid-May.

I have had a few people tell me about flying in one airport and out of another, so maybe I should look further into that.

My reasoning for going to Rome first and not last is that I know myself enough from past trips that my energy dips a lot toward the end and I’ve been told that Rome is busy and chaotic and if I were to save that for the end I think I will be too tired to enjoy it, especially for as many days as I will be there (4-5).

Capri, Paestum, and Herculaneum interest me immensely, so maybe Naples is where I should put my extra day. I’m a major history buff/nerd and love anything to do with ancient civilizations (I plan to go to the Etruscan caves at Orvieto).

Is there an alternative itinerary anyone would suggest with all the details I have given? I’m open to suggestions.

I have had a few people tell me about flying in one airport and out of
another, so maybe I should look further into that.

This is called an open jaw or multi-city ticket- usually under advanced search on the airlines site.
Do not book 2 one way tickets.

Consider flying in to Florence, out of Naples putting Rome right in the middle.
Or vice versa

That makes sense, and if the open jaw flight does not work out, don't sweat it too much. Sometimes it is nice to return to a place and see one last thing you missed or just stay in a different neighborhood.
Putting the extra day in Naples sounds like a good bet.
A day trip you could look into in Tuscany is Volterra for Etruscan museum. Many of the Etruscan sites require a car but that is one that does not.

I see you have reduced the number of nights since the 1st iteration.

If you can do a multi-city ( aka open jaw) routing, flying into Rome and leaving from Naples would save some back tracking and an extra hotel change. It might be a little more than r/t to Rome, but your time has value.

So this might be possible:
Rome 5 n
Florence 4n
Orvieto 2n
Naples 4n

I would add a day trip to a hill town in Tuscany, Pisa and Lucca are lovely, but a place like San Gimignano or a Wine Day out to the Chianti Region would be easy from Florence. Italy is such an incredible place, no matter what you do, it's all good.