WIthout knowing your interests, it's hard to recommend which stops or even which route to take.
Are you doing the Venice-Assisi drive in one day, or would you consider staying overnight along the way? Ditto for the Assisi-Rome leg?
Driving from Venice to Assisi, you could go via Ravenna if you're particularly interested in the Byzantine empire. The mosaics are spectacular and unique, but to visit there will take you a few hours. The more direct route through Bologna and Florence will be more on main highways. South of Florence you could stop in Colle Val d'Elsa (known for crystal) and Siena before heading southeast via Perugia.
From Assisi to Rome, if you headed west via Montepulciano and Orvieto, those towns are popular tourist destinations. However, on the direct route south of Assisi is Spoleto, which is also popular (though not on main highway).