In general terms, south of Sicily has so much more to offer than north half of island, the same as easter jewels definitely beat everything that you can see on the west. So, if you have limited time to stay on the island of ancient gods, best is to opt for a route from Messina down the coast and then at least until Agrigento...
This ancient jewel of stunningly reconstructed ancient Greek temples - called "Valley of the Temples" - boasts on bare, rocky hills heading over big and not much tempting city of Agrigento. You can definitely skip the center and go straight to UNESCO enlisted complex where, especially at the sunset, atmosphere of divinity and historical greatness are enthralling. We were lucky to witness a wedding session of Sicilian couple on the stairs of Temple of Juno - famous place for newlyweds blessing.
Most spectacular of whole the park, that needs at least two hours to fully be appreciated, is Temple of Concord - almost impeccable structure that dates to 5th century BC. However, you will also not be disappointed by impressive fragments of columns, portals and even bath tubes scattered all around the area. Not only for ancient history lovers :)
There is really splendid camping nearby with unusually good bathroom facilities (as for Italian standards), moderate prices, neat bungalows if you mind tent and even swimming pool. Otherwise, there are still some decent, budget wise BBs around like Oceano & Mare at the very sea side or beautiful but relatively cheap hotel Belvedere.
Finally, as you already have seen the ancient temples and feel like sea fun, 15 minutes driving from Agrigento there is immense white limestone rock named Scala dei Turchi, after Turkish pirates invasion. It's favorite place for suntanning and... photographing with nice beach and really spectacular whipped cream like shapes rising over the sea. It's easy to climb, pleasant to lie on and usually quite populated.