The perfect Itinery

If you have 10 nights and want Rome, Florence and Palermo only
I would divide like this:
Rome 4 this is the bare minimum here IMO
Florence 3
Palermo 4

Best route would be to fly into Florence and out of Palermo ( none of these will be direct flights)
Look for multi city” flights (not 2 one way flights)

Take note of how long it takes to get to and from Palermo from mainland Italy

A 4 night stay gives you just 3 full days in location

Most of your other questions would be answered in a good guide book

Read thru info here and in this forum as well

https://www.ricksteves.com/europe/italy

Note April 20 is Easter 2025

Don’t worry about looking like a tourist, they will know you are no matter what you wear!
(jeans are too hot and heavy for us)

if 10 days ....

How many nights will you be in Italy?

Christine has come up with probably as close to 'perfect' an itinerary as possible with the given parameters.
Just hope you are not too price sensitive about airfare. Her routing is time efficient, but doubt it is the cheapest way to fly.

The US style of uber does not exist in Italy

April weather is lovely, in our experience. In Sicily, later can get quite hot. Can you manage to go for 14 nights? It will be a much more comprehensive trip.

Not sure what you expect in “5 star” hotels. The rating system in Italy is briefly explained below..

We are usually happy in a 3 star as long as we have an ensuite.

One star rating
Customers should be able to expect that the front desk is staffed at least 12 hours a day. The standard size for double rooms should be 14 square meters. Staff should clean the rooms once a day and change the bedsheets once a week.

Two star rating
A one star hotel bumps up to a two star hotel if it has an elevator and the staff cleans the sheets at least twice a week.

Three star rating
A three star Italian hotel contains features and amenities consumers can expect from a modern establishment: reception must operate 16 hours a day and the receptionists need to speak a foreign language, the staff and concierge need to be dressed in uniforms. Hotels of this rating must have a bar service and its rooms must have Internet and a bath.

Four star rating
A four star hotel must have its staff clean and reset the entire room once a day. This is usually done in the afternoons. They need to replace bedsheets and towels daily as well. The hotel must offer a laundry service. There must be as many parking slots as 50% of the total number of rooms. Room measurements also get upsized in this rating: a double room should be 15 square meters in size while the bathroom should be at least 4 square meters.

Five star rating
Five star hotels must have receptionists who can speak at least three languages. Reception should be open around the clock, 24 hours a day. Single rooms must be 9 square meters and double rooms must be 16 square meters to be considered as five star quality.

Oh! Thank you Laurel.
I've often wondered what the star ratings meant in Italy- never bothered to look it up- now I don't have to!

To get a good look at the highlights of Sicily (which are quite scattered geographically) at a non-hectic pace really requires at least 2 weeks if you are willing to rent a car for part of the trip. It takes a bit more time if you want to use public transportation alone, because Sicily lacks the express-train service you'll find between major cities elsewhere in Italy.

It takes a long time to get to Sicily from Rome by train, bus or even by car. You'll need to decide whether you're willing to spend that much time (twice) when you'll only have enough time in Sicily to see one or at most two small areas (Palermo and Cefalu in your case). You can fly, of course, but then you have the hassle of dealing with airports--something I don't like to do in the middle of a trip, especially such a short trip; it's the opposite of relaxing.

Unless you have a specific reason (such as family heritage) that makes visiting just the Palermo/Cefalu area worth the required travel time, I'd encourage you to make Sicily a trip of its own in the future.