Extra time in Naples or Palermo?

Lucky You as both locations are wonderful. I have done both independent of any tours and can say there is plenty to see and do. Review your itin with the tour then fill in with the Rick Steves guidebook.
You will not be disappointed. Palermo is still off most travelers radar. It can be enriched beyond.
Enjoy these great visits, maybe a little gritty in places but none the less terrific and memorable.

It will be easier and probably cheaper to return to Naples in the future (by train from Rome) than to revisit Sicily. There will be plenty to see in Palermo outside of what the tour covers. I don't think the tour goes to Cefalu, either.

My first thought was there's a lot to see and do in Naples, not nearly as much in Palermo. Then I read acraven's advice. Yes, spend your time in Palermo and Cefalu. Revisit Naples on your next trip to Italy, after you've been introduced to it.

I will give another vote for Palermo. We will be there (4 nights) in the fall for the first time. Based on positive reviews here we will do a day trip to Cefalù per train. We plan to visit Monreale (per bus) as well on another day.

What a fabulous itinerary and those are my 2 most favorite RSTs. Personally, I like not leaving the same day as tour end and as well, always appreciate an early start by minimum 1 night at the tour hotel. Having experienced each, I would want more time in both of these incredible, fascinating, distinctive and endlessly entertaining cities. I'm envious of the choice(s) you need to make!

Yeah, tough call though I don’t think you’d go wrong either way. Unless your tour doesn’t cover sights in Naples, I’d vote Palermo. Palermo kind of blew my expectations apart. While I loved Naples, Palermo is probably a little more enjoyable for a couple days. It can be similarly “gritty” to Naples, but by contrast I found Palermo to be much more grand and cosmopolitan. The city center is more “broad elegant boulevards” and doesn’t have that pervasive mania that makes Naples, Naples. Your tour probably covers the big sights, I’m imagining a couple chill days between intense sightseeing tours will be a good fit.