I can only really speak for the MN part of a Lake Superior tour. By early June along Minnesota's North Shore, you'll find the mosquitos and black flies are out. Bring strong bug spray. The flies are the worst - they don't seem to care about bug spray! If you left in mid-May, you'd probably miss the bugs, but it can get pretty cold at night.
If I were touring around Lake Superior, I'd go in September. The bugs are basically gone by then, but the days are still pleasantly warm and nights are cool but not cold. I'd also consider the traffic. The North Shore is a very popular destination among Minnesotans, which means heavy traffic on Hwy 61 following the shore. There's wide shoulder in some sections, and a great trail in a few sections, but there's also some spots with very narrow shoulders and very heavy traffic. Whatever you end up doing, have a great time!