Mothers day to Fathers day weekend is typically when they are at their worst depends on the winter snow pack. Black flies are trout food and they like cold clear water so they kick in soon after spring run off.
With respect to places to take a day off, the best suggestion is to try to schedule those days down in the valleys in the hardwoods. Even though the trail may be crowded it doesn't take more than about 300 feet between the trail and a spot in the woods where no one will see you. Most folks hike with their heads down not paying anywhere near the attention they should to what is going on to either side of them. Forget finding a quiet official campsite, there are far too many users who are going to be heading to them.