Ther are many close to the lake, if not on it. If you plan to visit Lake Michigan State Park.. Get reservations in and do it early.
Side note: Last time I was in that area I did not stay on the lake,, I stayed at a little campground off US-131 (Lake Schep-a-no_ or some thing like that) but I was there for another attraction: Blue Lake Fine Arts Camp.. North of Muskegon off 131 my daughter was there with the international band (And before that with a normal summer camp) Lots of very good music.. Those kids will surprise you with how good they are.
Later I was playing a Mini-Disc.. A music teacher thought it was a CD of the music store type.. No, it was all high school kids at Blue Lake.. I think the track was Montheau's and capulets,, Same track VISA used for one of their commercials (San Fransisco Symphony as I recall) and the kids were every bit as good.