Don't know the Ludington area, but I also highly recommend Pilgrims Village in Cadillac.
Lake Mitchell and Lake Cadillac are some of the first lakes to have safe ice in the area.
They have great fishing for Pike, real nice Walleyes, slab crappies, and decent perch.
Pilgrims village has everything you need for fishing. They have live bait, Rods, tackle, shelters etc.. and you can rent a cabin for six people that has a kitchen for a very reasonable price. You can even ice fish right out in front of your cabin.
I usually fish "Big Cove", "Blind Island", "Kenwood Park" or "The Slabs". Stop in to Pilgrims Village and they will show you on the map where these spots are located, recommend baits and even tell you how people have been doing and where.
Here is their website if you want to check things out:
http://www.pilgrimvillagefishing.com/Now the hard part to believe: I'm not a paid spokesman for them
What ever you decide, Have a nice trip and let us know how you did