One of the most beautiful parts of the Sicily in my opinion it is the part of Trapani and here is how I recommend you to pass 48 hours in Sicily. THE low cost flights to get there, here Easyjet and Ryanair are the masters but if you book well in advance also Alitalia is very valid with round trip to less than 100 € or if you leave from Rome you can opt for the Darwin Airline, which flies under Alitalia and offers low cost flights.
What I recommend as soon as you arrive, or even better already from home and online, is rent a car. Public transport is not the best and the distances are not very short, the car allows you to travel without problems reaching even the small beaches where you can sunbathe best.
One warning, if you take a rental car, always remember that a credit card is required and that it must be returned absolutely with full fuel, otherwise there will be a high penalty to be paid.
The tour of yours 48 hours in Sicily and in particular in the northwestern part of Sicily it can start from Trapani. Here you can take a tour in its historic center, elegant and beautiful, very popular in the evening by young people from the post with clubs and bars where to take some appetizer. To sleep in Trapani I recommend the Ai Lumi b & b, also valid as a restaurant or to make an aperitif with a good bottle of Sicilian wine.
A respectable dinner right in front of the sea and in Baroque style you can do it a la Taverna Paradiso, here the busiate with eggplant and swordfish are a must try. After a nice romantic walk along the Trapani seafront, you can reach the most extreme point of Sicily and enjoy the immensity of the panorama in front of you. For an unforgettable and typically Sicilian breakfast go to Colicchia pastry shop, granita and coffee with cream together with a good hot brioches are the best way to start the Sicilian day.
With the car you can go in the direction of Salt pans of Trapani, historical and very suggestive place to see. There are also several here wwf reserves that you can contact for sightseeing and educational tours. Another route that I recommend is to visit the magnificent city of Erice, also called the city of 100 churches. To get to Erice you can always proceed by car, the route is for the hard stomach as there are many curves but absolutely divine with beautiful views of the sea where you can stop and take pictures. Or take the cableway to Erice. In Erice you must not miss to visit the Cathedral of the Assumption and to try the Genovesi by Maria Grammatico, a true institution.
One last tip is to take the car and go to San Vito lo Capo. Here in addition to the beaches, you should definitely try two of the culinary specialties of the area, for a quick but very tasty snack. First of all the cold hot ice cream, then the delicious panelle and arancini di Frii and Mancia!