Liberty Market 95 Main St, Woonsocket, RI02895 Located on Main Street in Historic Downtown Woonsocket, Liberty Market sits between The Cakery and Harlequinn Costume…More Rentals. Although Liberty has only been in business since 2007, it has become more than just "the corner grocery store" to the customers who shop there. Aside from offering all the necessary items that fill the cupboards and refrigerator, Liberty also has an eight- top table in the center of the main room. Folks come in to shop but stay to gossip and watch the sports games. Ice cream, baby formula, DVDs, lottery tickets and a fresh pot of Starbucks coffee are also available in the store.