Thanks, Everyone: we can probably eke out 10-11 days since boys will have already taken the SATs. Flying into Palermo and out of Catania seems to be much pricier so we want to fly in and out of the same airport. We will rent apartments so that might help as far as things being closed. Easter week is when our boys have school break so that is the time we must go if we do go.
I have a couple of questions:

• 1. Easter. I know that could be tricky. We probably would land on Good Friday in Palermo and start our trip there. But Easter weekend!! Will all the sites be closed?
• Itinerary: know people don't recommend doing Palermo and Siracusa in such a short time frame, but we enjoy driving so another idea would be to land in Palermo spend a night in Trapani and then drive straight to Siracusa and work our way back to Palermo with a stop at Agrigento, then drop off the car at the airport and spend two nights in Palermo at the end of the trip.
• What we want to see: Palermo, Siracusa, Villa Romana, Agrigento and then something quiet.... rural. Thoughts?

Thanks for any insights

My reason for suggesting that you choose east OR west has nothing to do with driving times -- it has to do with the overall time you have in which to visit places with much to see. Even with 11 days, I might JUST be able to see Palermo, Siracusa, the Villa Romana, and Agrigento (assuming you actually have 11 on the ground); I certainly wouldn't have time for anything else -- and that would include Trapani, a more rural destination, or any of Sicily's other gems. YMMV.

And BTW, no reason to return the car at the airport: There are plenty of car rental drop off locations in Palermo itself.

Funny you should ask ... our family did two weeks in Sicily and Malta in April in 2017. It was one of our more memorable and enjoyable trips. We went Palermo -> Cefalu -> Enna -> Catania -> Taormina -> Modica -> Siracusa -> Malta -> Agrigento -> Sciacca -> Erice -> Palermo and I wouldn't change a thing. Palermo is a fantastic city, especially the markets, and very enjoyable to walk in. Your kids will have a blast climbing the Rock in Cefalu and the views are amazing. Enna and the interior are fascinating and less touristy with incredible landscapes. Catania is an underappreciated gem with even better markets than Palermo and a beautiful university campus. Erice is breathtaking. Two weeks was enough for us to feel like we could see all the highlights of both islands, but judge for yourself!

OK besides worrying about things being closed Easter weekend... I have to remember my teens get tired of ruins and churches....... I could look at them for weeks. So we are looking at hiking near Trapani (stay in Trapani? or elsewhere?)
Wonder if anyone had any "experiences" they thought were memorable that teens might like. For instance, I saw a Falcon training demonstration but that was in an area we aren't going. Any memorable walks. Memorable agritourismo? Something so my kids don't roll their eyes and mutter: "another ruin?"

We have a May trip planned...I'll start my own thread soon, but here is the itinerary.

(The flight plan was constrained by the fact that we used miles, and an initial paid nonstop from Madrid to Catania got cancelled one week after we booked it. It obviously would have been more efficient to fly to/from Sicily on a single same-day connection, but, alas, that was not to be.

God, I hate mileage plans -- they get worse every year...fewer miles earned each paid flight and more miles needed each free flight. I may just switch to a cash-back card and pay a little more each flight for decent boarding.)

Anyway, back on topic...

PHL-- FCO (change planes in MAD)
Rome 1 night in an AirBnB in Trastevere near Tram 8 for easy next-day train access to FCO.
FCO-CTA and bus to Siracusa - get there in late afternoon.
Siracusa 3 nights (basically two days) in AirBnB.
Drive to Agrigento first thing in the morning and see the Valle dei Templi in the afternoon & evening.
Agrigento 1 night in a hotel near the Valle dei Templi.
Drive to Palermo
Palermo 3 nights (two and a half days) in Air BnB.
PMO-FCO
Rome 3 nights - we've been to Rome three times before and love it, so for us this is a cool place to spend some time before going home.
FCO-PHL

I know it's a lot of time in transit...very unlike our usual trips where we have one or two "base" cities -- but we had little choice.
Please -- no cirtiques here. I do not want to hijack this thread...just wanted to give a sense of what we felt was good to see in what is essential a week in Sicily.

ssander

I just want to add two things:
Our experience in Italy at Easter was that most places were closed both Sunday and Monday. Only the bars were open. If you have an apartment, stock up on food before the weekend.
I also want to second the suggestion of Taormina, since you seem to be not including it in your itinerary. It would be a good day trip, although I would love to stay there. I know people who went there for several weeks and took Italian classes or cooking classes and loved it!