Walleyes are located at different parts of the lake at different times of the winter. Some lakes the movement is more pronounced than in others. (Tip: If you can, take a boat with a fish finder and mark the bottom types on the map, ie stone, sand, muck, weedlines and how deep and far they extend. Only has to be done once. This will help you select your spots during different times of the year.) . Without knowing the bottom type of the lake survey I will give you my suggestions assuming that most of it is stone or gravel
Early season and black ice I typically find them in fairly deep water 30 ft plus so the northern most island is ideal because it is a fairly shallow area but with close access to deep water. If the 50 to 60’ foot area is a muck bottom target the opposite side of the island. Also any points with sharp drop-offs to deep water should be targeted.
Middle season, ice is opaque possibly some powder snow is on it , I would target the southern most point on the island by the two boat launches.
Late season, ice has had snow on it for considerable amount of time and light penetration is minimal and is possibly honeycombed due to thaw and re-freeze, I would target the cove on the northern most part of the lake or to the left of it. Looks like prime spawning area if there is a gravel bottom and an inlet stream. Late season I also like to fish shallow as well, less than 15 feet of water. Some of the largest fish I caught were late season females about to spawn. Don’t worry, they were all released, have to make sure there will be more for the future. Besides I’ll have the additional pleasure of catching them in the summer, then they will end up in the frying pan.