Independent travel is a real possibility in Sicily and - despite what some "Sicily experts" may imply - it doesn't necessarily entail renting a villa in Sicily for two thousand euros a week or staying in deluxe seven-star hotels. In fact, it can be reasonably economical. Here are a few ideas to get you started.
Sicily Concierge and other, similar firms can help plan a personalised itinerary. This service need not by unnecessarily expensive, and it offers the advantage of a specialised travel agent. (Full Disclosure & Reality Check: Sicily Concierge advertises on Best of Sicily but they are often consulted by the concierges of certain major credit card companies, often before these companies' "official" travel service representatives in Sicily are even queried.)
Best of Sicily's hotel page makes hotel reservations easy and efficient (through use of a highly-sophisticated network), and the site itself is full of travel tips. It's a destination and travel guide, after all. There are also "niche" services like Sicily Moto Rent, which rents motorcycles a week at a time.
Another interesting idea is the flexible travel "package" offered by Sicily Open Voucher. The focus here is hotel reservation options linked to your car rental and, of course, flexibility in your independent travel around Sicily.
"Independent" travel doesn't have to mean that you're always "alone." If you're looking for local tour guides for an excursion or day tour, consider a service like Palermo Guide or Eastern Sicily Guides.
Best of Sicily and the firms mentioned here have no monopoly on this field. There are other travel consultants and firms which can provide similar services. What's important is that you consider your choices.
I'd like to make a point here, and it reflects a sentiment which I know isn't really shared by all "travel experts." Much as I respect the effort and dedication of Sicilians who live and work outside Italy, the firms mentioned here are actually based here in Italy, so they help support the local economy directly. That's important because Sicily isn't just a place. It's people too.