Itinerary for Sicily

I had the same idea as you but gave up on the (Valletta) ferry because I didn't have any confidence that I'd be able to get to Siracusa easily from Pozallo. The bus service did not seem coordinated with the ferry, unless you were taking a tour through Virtu Ferries (which looked like it ran its own bus service for the tours). Pozzalo is on the Trenitalia Regionale train line, but it's a tiny beat up looking station and you're at the mercy of the train schedule (not impossible but requires flexibility). I opted to fly Malta Air to Catania - it was an inexpensive, 40 minute flight. From Catania Airport, it's very easy to get to Siracusa without a car - there are cheap and frequent buses that go straight from the airport right into the city.

Even if can you rent a car in Pozallo, how are you going to bring it back there? They may not allow drop offs elsewhere because it's such a small place (and they probably don't have a large fleet to choose from). You have to confirm this. Just use Google or look at Google Street view to find rental companies. I could not easily find anything with a quick search. Good luck. In worst case, a cab can bring you to the train or bus station if the car rental doesn't work out.

I Googled "car rental Pozzallo" and got hits--mostly Brand X but also an indication that Hertz may be there. (Note spelling; you may have difficulty with your routings if you aren't careful.) I didn't delve any deeper. Have you tried consolidators like AutoEurope and Gemut?

I think your trip will not be too rushed in general, though I haven't looked at the ferry schedules for the Lipari Islands.

I noted from a check of the map that Pozzallo is down in the SE corner of Sicily, so I want to point out that there are some really gorgeous Baroque towns down there you have time to see. If (not a minor point) you rent a car with an enclosed trunk and can put all of your luggage out of sight, you could make one or two stops on the way to Siracusa. Still, it would be prudent to carry any pricey electronic gear with you if you are out and about. This is not a comment on Sicily in particular, but rather a warning about what can happen to cars parked near tourist sights just about anywhere.

The top stops in the SE corner (aside from Siracusa itself, of course) are Ragusa (which involves a lot of walking and could use a whole day or overnight), Modica, Noto and Scicli. Some of those could be visited during your time in Siracusa. Inland Sicily is really pretty, and I urge you to see something besides coastal cities and islands. In addition to the places I've just mentioned, the area around Piazza Armerina and Enna has some worthwhile sights that would not be terribly far off the logical driving path between Cefalu and Agrigento.

I haven't been to the Lipari Is. and cannot comment on availability of lodging, frequency of car ferries (if any), etc.

Cefalu isn't terribly far from Palermo and if you wanted to, you could visit it from Palermo by train in one day, which would reduce the number of hotels by one. Cefalu would certainly be a more peaceful place to spend the nights, though. Cefalu is tiny and in a pinch I think you could get by with one night there.

As you move from Agrigento to Segesta to Palermo, try to find time for at least Erice, an extremely atmospheric hill town above Trapani. Trapani itself is nice, but that might be too much.

Choose your lodgings in Palermo carefully. You do not want to have to drive through the city proper. There are many vehicles and not enough traffic lights, for one thing. Actually, I'd try to visit Monreale on the day I moved to Palermo, and then I'd seriously consider dropping the car immediately.

I have daytripped to Stromboli from Lipari, which I think is a better base and has more to do if you are going to spend a night. Driving to Milazzo to catch a ferry the same day can be iffy (the ferry I took had one departure in the morning, one at noon and one in the late afternoon; the noon one was not convenient for spending any time in Stromboli and making it back to Milazzo the same day, but that was in 2013 so perhaps there are more options now).

I think you are trying to pack in too much on certain days, especially travel days. Other than that it seems doable to me.

I also think it would be best to fly to Catania and rent a car at the airport there, returning it when you get to Palermo. Or use the buses to see Taormina, etc, then pick up a car somewhere in the area for the rest of the island. Syracuse is worth a day or two for sure. On the way to Agrigento, stop to see Villa de Casale (maybe a night in Piazza Armerina). Add Selinunte to your Greek temple visits. You will neither want nor need a car in Palermo. Take the bus to Monreale from the train station. You can return the car in a Palermo city location, before or after dropping your luggage at your Palermo hotel for storage. Then take the train to Cefalu (with a small overnight bag).