Although it will be different in smaller towns, you can generally eat any time of the day in larger towns and cities, including Verona and Venice. There are cafes and tavole called, or "hot tables," more like a cafeteria. Also, pizzerias in many areas are open throughout the day. Restaurants in the more "touristy" places will be open longer hours to accommodate foreigners.
However, the more traditional restaurants tend to be open during the lunch hour--noon until about 2:30--and the dinner hours, which generally begin around 7:00 p.m., and continue until late. This is where the better dining experiences will be had, and it seems to me that traditional dining is a real part of the cultural experience. Consider: Your internal clocks will be all messed up anyway due to the jet lag. Why not eat when the locals eat, where the locals eat? Your children will love the experience of eating outside AFTER the sun has gone down (mine did) even though the meals generally lasted past their bedtimes. Another consideration is that many places close for the lunch hour and reopen later in the afternoon. Adjust your rhythm to coincide with the local rhythms. You'll become a local for a time.
