For this itinerary, given the amount of possible activities, we suggest you to follow the state road towards Palermo to the Buonfornello junction, then reach the capital on the highway, but also the state road reserve pleasant views (with the unic exception of the industrial agglomeration east of Termini Imerese).
It is difficult to suggest what to see in Palermo in a day, because a week would not be enough.
A possible strategy could be to start from Monreale (which is located south of Palermo can be reached bypassing a bit ‘of city traffic), with its cathedral, the cloister and the view over the city of Palermo, then, depending on time, choose what to do, perhaps helping by a guide, for example parking the bike or the car for a sightseeing. In this case you can take the buses close to Piazza Castelnuovo (motorcycle parking at the end of Viale Libertà right) and going to stop in Via Emerigo Amari (for cars there are private parking in Via Trapani, Via Agrigento, near the Court in Piazza VE Orlando and within the port area, by road you can park for a fee 1 €/h but between 9 and 19 it’s difficult to find a parking).
Parking the vehicle in this area, after the end of the sightseeing tour, you can start exploring the historic center (it is said the largest in europe) along Via Ruggiero Settimo.
We suggest to enjoy Palermo in the evening, staying for dinner, take a walk downtown in quiet, and postpone to return after dinner at the signalman’s lodging 59 + 866.
A possible alternative, or your possible second day in Palermo, can provide parking in the area of Piazza Indipendenza (descending from Monreale or taking the exit “university” in ring road), a visit to the unmissable Cappella Palatina (access from Piazza Indipendenza), perhaps with a tour to S. Giovanni degli Eremiti, and starting a walk along the Norman Arab route passing under Porta Nuova (or if S. Giovanni degli Eremiti will be part of your tour by turning right to Piazza Vittoria instead to go back towards the entrance to the Palatine Chapel).
By this tour is possible to view the Cathedral, along the old course of Palermo, called the Cassaro (today Via Vittorio Emanuele) to admire the old noble residences, down towards the “4 canti” and, turning right, on Via Maqueda up to the fountain of Piazza Pretoria (called shame place for the naked statues) with the city palace that looks sternly, completing the tour with one of the few examples of Arab architecture, the incredible church of the Martorana, with its red domes and its Greek writings.
In short it is really difficult to contain in a few lines suggestions for Palermo, the Serpotta speakers would be out, really amazing, the countless churches, the “Palazzina Cinese”, the interior of the Teatro Massimo, the alleys of the historic center, the interiors of the noble palaces as Palazzo Federico, the incredible chamber of wonders recently discovered, the botanical garden and Villa Giulia, and so on, really every visit to Palermo can only be a advance, a partial visit for subsequent returns. If your visit is not in July and August (a period of great overcrowding of the seaside areas) among the various possible visits you can not forget the seaside villages of Mondello and Sferracavallo, for pleasant baths, panoramic aperitifs and excellent meals based on fish.