Michigan Summer Vaca

My small family- husband, 9 yo son, and small dog will be traveling from upper Wisconsin to Mackinac Island and then down south along the Michigan Lake shore in mid July. After spending a day on Mackinac Island, I want to find a place to settle for a few days- beach activities for my kid, and town activities for my husband and me. I was thinking of staying closer to Traverse City, but I’m worried the water will be too cold. My kid will be used to upper Wisconsin lake temps, but do we need to go more south to enjoy the beaches?