Just outside Whitefish Point (which I bet will be very busy on the 4th, BTW) there's a sweet beach and nature reserve that takes some dedication to get to. Probably won't be crowded at all. https://maps.google.com/?ll=46.76132...97589&t=h&z=14
Mouth of the Two Hearted (rustic campground here but might be full). If you go here you will see all of the leftovers from the forest fires last spring. Pretty crazy. https://maps.google.com/?ll=46.69852...48795&t=h&z=15
Gotta see Grand Marais if you haven't yet. Get a beer at Lake Superior Brewing Co. https://maps.google.com/?ll=46.67818...97589&t=h&z=14
There's a really scenic road now between Grand Marais and Munising.
Chapel Beach. Amazing. It takes a hike to get back there (including both the dirt roads and the hike itself) so that deters some people. NO DOGS ALLOWED
Sandpoint beach in Munising. https://maps.google.com/?ll=46.45355...24397&t=h&z=16
Kinda pricey but the guided sea kayak tours of Pictured Rocks or Grand Island (depending on weather) are awesome. http://www.northernwaters.com/
Hotel in Munising that is nice: https://maps.google.com/?ll=46.44007...12199&t=h&z=17
Lots more to the west if you are going that far. As for camping, make sure you get the Mi DNR camping app. It shows all of them. First come first served on them though so it could get tight on the 4th, but I bet you can find something.