Stand anywhere and five distances are fixed: one to the water's edge of each Great Lake. Here is where you can make the nearest few of them as small as they will go.
Two lakes cost nothing. Lake Michigan and Lake Huron are one body of water joined at the Straits of Mackinac, so their shores meet and you can stand on both. A third lake costs 25 kilometres. A fourth costs 237. The fifth, only 35 kilometres more, is the one that moves the answer out of Michigan and into Ontario.
At each of these spots the lakes that matter come out equal, to within a few metres. That is what a best point looks like. If one were nearer than another you could still walk toward the far one and improve, so you would not be at the best yet.
Not one of them beats an empty stretch of the Bruce Peninsula. Duluth sits on a Great Lake and is still a thousand kilometres from its fifth.
Shorelines are the five lake polygons as drawn in OpenStreetMap, which keeps Michigan and Huron separate at the Mackinac line and counts Georgian Bay and the North Channel as Lake Huron. Standable ground is the full-resolution GSHHG coastline with every inland lake taken out and every island in a lake put back, so Manitoulin and Drummond and Isle Royale are all fair places to stand. The search grids the whole basin at two kilometres, then closes in to five metres. Distances are true geodesics on the WGS84 ellipsoid.
One judgement call matters. OpenStreetMap draws Lake Huron a short way up the St. Marys River. Cutting that arm off at De Tour Passage moves the three-lake answer 600 metres and changes its number from 25.3 to 25.6 kilometres, so the finding holds either way.