How remote are we talking? Theres lots and lots of great places in MI, north of Saginaw and Grand Rapids that would be quite remote but still near enough to amenities.
Cadillac area is a great option, close enough to US 131, enough places nearby that you can get supplies,but not as built up and expensive as the Traverse City area. Its not on the big lake but there are a million little lakes in you want water.
Years previous my wife and I stayed at Meemos Farm in Evert, nice modern cabin on a private lake. Its pricey but really nice. There's millions of other places on Air BNB. Avoid the Boyne Mountain, Shanty Creek area in the winter time, unless you're looking for ski opportunities, as its crazy expensive.