Sicily itinerary

Erice for sure.
If you go to the valley of the temples already, then maybe you can skip Selinunte. It’s a large site, so it would take too much time to see temples that are not as well preserved as Agrigento or Segesta. Maybe see the temple of Segesta which is nice and small enough for a short visit.

3 nights in Palermo is good, but if you want to squeeze in Cefalù then you don’t have much time left for Palermo. I presume you would want to see also Monreale on the hill above Palermo.

For the best restaurant in our two week trip to Sicily, check out the link below.
About 45 minutes south of Taormina, we were starving for pizza. We googled and found this (very humble from the outside!) restaurant. We had a hard time finding the entrance, and only the takeaway was open (mid afternoon). Decided to go for it. They welcomed us as only Italians can, helped us choose our food from the delectable takeaway case, and made space at a tiny table for two and brought us wine and our hot food. While enjoying our meal, many locals came through, purchasing their own favorite goodies. I'd love to go back and eat in the full scale restaurant, but even the takeaway was magnifico!
The full name is : Ristorante Pizzeria De Natale Angelo
https://www.angelodenatale.com/

P.S. There is an express train from Palermo to Cefalu. We did a day trip (opposite direction) and it was much easier than taking the car. Enjoy!

Looks like a wonderful itinerary!

Based on our 2022 trip to Sicily —

Favorite restaurants:

Palermo - Procopio Pizzeria, La Galleria

Ortigia - Trattoria La Pigna

Taormina - La Locanda Dei Moro (snacks, burrata salad)

Favorite sites/experiences:

Valley of the Temples at dusk

Monreale

Emilio Sciacco winery for tasting and view of Mt. Etna

Greco-Roman theatre in Taormina

Wandering Palermo in the evening

Missable:

Cefalu - crowded, touristy, unwelcoming

All in all a solid itinerary. For what to see en route to Palermo? I think you’ve outlined some good options. If you’re ruins-crazy, then I’d vote for Selinute. Haven’t been, but it seems underrated in the shadow of Valley of the Temples. Trapani-Erice seems “most different” in the itinerary. Still, by some accounts it’s pretty touristy. I would consider Erice to be rather weather dependent. I’ve heard it can get messy or socked-in when the weather gets iffy. You can play this by ear.

In Siracusa, if you can stay in Ortigia I would do so. It’s really one of Sicily’s highlights, and its main square is buzzing at all times. Though it has the Archeological park, Siracusa isn’t anything special. You should be day-tripping from Ortigia to Siracusa. If you’re into archeology, the Museo Paulo Orsi is one of the best. It made the museum at Agrigento feel pretty weak and redundant.

I can’t recommend specific restaurants, but make sure you order anything and everything that contains ricotta, pistachios and/or almonds. It’s mind-blowing here. Cannolis are at their very best when they fill them to order, like in a restaurant versus a bakery. Enjoy!

If you don’t like beaches, I would skip Cefalu since you hardly have any time in Palermo. I was recently in Palermo in May for five nights. The details are about halfway down this trip report:

https://community.ricksteves.com/travel-forum/italy/my-1-month-independent-trip-to-southern-italy-tribute-to-my-husband

I didn't visit Taormina. I've seen mixed reviews on the Forum.

I stayed in Ortigia, which is the old city of Siracusa. It was lovely. It was also easy to drive in and out of Ortigia on day trips.

I stayed in Piazza Armerina between Agrigento and Ortigia (I went west to east) to visit Villa Romana. I regretted not having more time to see the historic center, where I spent the night. I had a couple hours in the evening and again in the early morning before going to to Villa Romana.

I went to Segesta and Selinunte before Agrigento. Segesta only takes an hour or two and is worth seeing. I spent the better part of a day at Selinunte and liked it better than Agrigento. Because it's so spread out, there aren't any crowds. Agrigento is compact and, yes, the temples are "better", they are all in a row. My visit was at the end of April and the only places that were crowded were Monreal in Palermo and Agrigento.

I spent 2 nights, one full day, in Cefalu (round-trip from Palermo). That allowed me to enjoy the early morning and sunset on the beach and have time to wander the historic center.

I took the bus from the piazza at the Palermo train station to Monreal. Don't miss the charming cloisters. On the way back the bus stops at Capella Palatina. From there I did a self-guided walking tour back to the center. One very full day.

I didn't visit the Greek ruins in Sicily, but I wonder whether you need 3 nights in Agrigento. I don't think there's much there besides the ruins, and I don't recall other itineraries with such long stays there.

Taormina is very touristy and quite expensive. I was happy to leave after 2 or 3 hours. Be sure you will find enough to interest you to justify spending 3 nights there.

There is just so much else to see in Sicily. In the area around Siracusa, I liked Ragusa, Modica and Scicli as well as Noto. Since you'll have a car (I did not), it would be relatively easy to see those Baroque towns if you could afford the time. As already mentioned, Palermo deserves more than 3 nights, especially if you're going to visit Cefalu.

Many thanks to everyone who replied. Special thanks to Roberto. After reading all your advice, I am considering staying only 2 nights in Taormina (we are actually staying in Giardini Naxos), and adding that night to Siracusa. As mentioned, unfortunately we can't stay longer in Sicily as our outbound flight is already booked, but we will have to leave something to see for a future trip!