Your comment about Finger Lakes was confusing to me; I looked it up and, amazingly, there is a tiny lake called Finger Lake in Ottawa NF near Watersmeet. Coincidence? Or did you get a little scrambled between MI and NY?
I grew up in MI, and we moved to OK 30 years ago. Along Lake Superior it can get quite chilly in June (heck, sometimes it's chilly in July!) from all that cold water. Farther inland it is warmer. Just figure on moving to a part that suits you for temps, because it can vary from day to day. Mosquitos can be thicker in June, too, but not usually so bad as to drive you out. Biting black flies along the shore are unpredictable and in pockets; if you hit a spot where they are, often you can go 15-20 miles down the road to escape them.
I have enjoyed the west unit CG of Porcupine Mountains SP, where one can walk a trail along one bank of the river, cross a bridge, and walk back along the other side; there are 3 waterfalls along the way. The east unit has a great view up high of Lake of the Clouds down below. A bit to the east of that, Ontonagon has a nice municipal CG on the shore, too.
McLain SP certainly is nice, if you can get a campsite. It's pretty busy. It's nice to bike or walk around the CG and then down to the south end of the park where there is (or was?) an ice cream shop. The drive along M-26 north to Copper Harbor is scenic, and I think people are welcome inside the monastery at Eagle River. If you like raspberries, see if you can pick up some of the local thimbleberry jam (if any is left from the previous year). Ft. Wilkins SP (as well as Fayette SP along Lk Michigan) have historic buildings and stuff to look at.
Personally, I like being up that way around August 1st when the raspberries, thimbleberries, and blueberries are growing wild along the shore area.
Speaking of Fayette SP, if you're down that way near Manistique, be sure to stop at Palms Book SP and see the Big Spring. The water is crystal clear, 40 feet deep.
Of course, the boat ride along the Pictured Rocks shoreline from Munising is entertaining, but you want to get a sunny day, and preferably take the 'sunset cruise' for best light on the rocks. Tickets are pricey, but it's worth doing one time anyway. I've read that the NF CG west of Munising (Bay Furnace CG) is nice.
Farther east, Grand Marais has a nice CG. Also Brimley SP near the Soo. Tahquamenon Falls and Whitefish Point have already been mentioned. If you get as far as St. Ignace, cross the Mackinaw Bridge and do the tourist thing around Mackinaw City; there's a fort and a couple of lighthouses to see, and fudge and trinkets to buy. Be sure to go to the local bakery for the best cinnamon bread ever, and some of their pecan rolls. Yum. A boat ride to Mackinac Island makes a nice day trip, but know that it will be at least 10 degrees cooler on the island as well as on the water, so take coats. If you have bicycles (or want to rent some over there), a ride all the way around the island is great fun (no cars, period).
Mike G.
Liberty is meaningless where the right to utter one's thoughts and opinions has ceased to exist. That, of all rights, is the dread of tyrants. --Frederick Douglass
photo: Yosemite Valley view from Taft Point