Health-food seekers and foodies alike love the Moscow Food Coop (follow Third Street right through Main and go two more blocks; turn right into the mini-Mall opposite the City Hall parking lot).
You don't have to be a member to shop there, but you save on some items if you join. They have local organic produce, canned and frozen goods and a wide variety of dry foods sold in bulk. This is the best place to buy spices and dried herbs: much cheaper than in the grocery stores: you can buy exactly the amount you need, and they are usually fresher, too.
They also sell meat, including free-range chicken and fabulous local lamb (expensive, but worth it). Sage Bakery breads and their own baked goods are available, as well as a variety of tasty take-out items. This is another great place to eat a quick and tasty meal before an evening event.