Dave.
In terms of ease of driving in Italy it depends on what you are used to.
Traffic in Italian cities is very similar to Manhattan traffic, therefore if you are used to that, you'll do fine. However, like in Manhattan, a car in Italian cities is not of much use. Parking is expensive and public transport is more efficient. Also, unlike Manhattan, the historical centers have been totally pedestrianized, therefore you can't drive there at all.
Driving outside cities, in the countryside or on a freeway, is not any different than in similar types of roads in North America. However Italy is largely mountainous and hilly, therefore country roads are more similar to the ones in the Rocky Mountains or Appalachia than Illinois where it's all flat. Driving at the Cinque Terre presents similar challenges. Roads are curvy and narrow, traffic is forbidden inside the villages, parking is scarce and parking lots are available only in Monterosso or Riomaggiore (the other villages have parking for residents only). Since the CT villages are connected by a rail line tunneled through the cliffs, it's much more efficient to use trains than the car, therefore at the Cinque Terre, your car will definitely stay parked in the lot the whole time.
In terms of visiting the towns you mentioned (Parma, Modena, Lucca), they are all mid size cities (under 200,000 pop). Traffic is restricted in the historical center of all 3 however, therefore you will need to park in a lot/garage outside of the historical center and visit the old town centers on foot.
If you intend to make stops along the way, it might make sense to use the car. However you might consider returning the car in La Spezia (next to the Cinque Terre) and go to the villages by train, so that you save rental charges and parking fees at the Cinque Terre where your rental car will just gather dust in a lot.