There are many small towns within that area Empire, Maple City, Cedar, Leland all of which have places to purchase groceries. Traverse City is a drive from that area but offers a whole lot more, they are a larger city.
Cedar is fifteen minutes away and has a good meat market and Traverse City is about 35 minutes away. Leland is 20-30 and has a nice wine store called Verterra and good shopping, at least through Fall.
Glen Arbor is a nice little tourist town, as well as the towns mentioned above there's also Glen Lake. It just depends on what you are looking for and what time of year you visit. Feel free to ask more specific questions and someone will surely answer.
My pick is Leland. Good shopping and a couple of good restaurant. Empire is great in late Sept for peaches and apples.
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