Summer (June–August) is peak season. Lake Michigan beach weather arrives in late June when the water warms enough to swim — before that, the lake is cold even when the air is warm. July and August are the best months: long days, warm water, the state park beaches at their best, and Michigan's Adventure in full operation. Expect crowds at the beach on summer weekends and book accommodation early. The Lake Express ferry to Milwaukee runs from May to October.
Late spring and early autumn suit those who prefer quieter visits. May and early June are pleasant for the waterfront museums and Victorian architecture without the beach crowds. September is often the nicest month of the year — warm enough to swim, fewer people, good light on the lake, and the colours starting to turn inland.
Winter has its own appeal. Muskegon State Park operates one of the only public luge tracks in the United States from roughly December through February, and the trails through the park are excellent for cross-country skiing when there is snow cover. The city is quiet and the waterfront museums remain open on reduced hours. Come for the luge, not for warmth.
Spring (March–May) is the shoulder season: the lake is cold, Michigan's Adventure is closed, and the beaches are empty. Good for the museums and Hackley-Hume tours if you want to visit without competition for parking.