Most of the lakes north of Grand Marais have good populations of decent sized pike and probably some good ones at the lake your staying at. June is not late at all for pike which can be caught all year round. The best places to look for are your quick dropoffs to deeper water adjacent to weed cover, thats where you'll find actively feeding fish sitting in ambush mode. If you use sink tip or sinking line you can probe the deeper water adjacent to the weed beds where the weeds stop growing. This is where you'll find alot of the bigger fish cruising around or laying near the bottom. 30"+ northern pike do not like warm water. They still can be caught shallow, but they won't be far from deeper water which means cooler water. Big northerns will lay in shallow water near the bottom if they have good ambush cover and the water stays much cooler then the surface temps. A key for growing big pike is deep cool water and good feed nearby.
Barry's pike flies, Whistlers and Decievers are all good flies to throw at them, red/white, chart/white are good colors anytime.
Late afternoons are prime times for top water in the shallows. Pike activity usually tapers off when the sun goes down.
There are hundreds of lakes to choose from in the area you'll be at. You can even venture to the edges of the BWCA by canoe with alot of those lakes holding good number of pike, plus you'll have lakes with smallmouth, largemouth, splake and laketrout. Choices are limitless up there.
Good luck!