I stayed at Hotel Ambasciatori on via Roma in Palermo. It was a good location for me - easy, level walk of about 5-7 minutes from the train station, very close to the Ballero market. It was basic but adequate, though I think I was in one of the poorer rooms. Breakfast was indeed served on the top floor and there was a rooftop patio with a view - it was too cold and wet in February to sit outside, though. It's a restaurant - had dinner there on one of my 2 nights. The food was very good and the service was too. The bus to Monreale leaves from the plaza in front of the train station. On the way back from Monreale, I got off the bus near the Palatine Chapel and did a self-guided walking tour. Palermo is very walkable. The immediate area of the hotel is quiet in the evenings - not much in the way of shops and restaurants. I believe there are a couple of good restaurants less than 10 minutes' walk, but I didn't try to find them.
I picked up a rental car when I left Palermo, at Hertz. In spite of many warnings not to drive in Palermo, it was quite easy and not very far to drive from there to the highway. I found it very easy to drive in Sicily.
I stayed in Castellammare del Golfo (rather than Trapani) and visited the temples at Segesta and Selinunte as day trips. I drove to Agrigento in the morning, including the museum, then continued to Piazza Armerina for the night. The historic center is well worth at least a couple of hours. From there I went to the Villa Romana del Casale (not to be missed!). Then I drove to Siracuse (Ortigia) for the rest of my stay.
After my 2 nights in Palermo, I left most of my luggage at the hotel and took a late afternoon train (with an overnight bag) to Cefalu for 2 nights, returning on a morning train to pick up my luggage and the car. I really liked Cefalu and there's a great beach there.
In the Trapani area, the towns pretty much shut down on Sundays. It's a good time for people-less photos, but not for much else. None of the wineries were open.
The only day I regret was the day I drove to Etna. Visibility was poor and it's really expensive to take the cable car.
I didn't use any guides. Some of the sights provided audio guides and I had some written information with me. I also bought souvenir guide books at some of the sights and used those too. At Agrigento, I think a personal guide would be worth it, but at the other places, not so much. I'm not a big fan of guided day tours, but if you won't have a car, you will have to use them.
