For the most part, big box stores and malls will be closed on Thanksgiving Day. Freehold Raceway Mall and Ocean County Mall will both shut their doors on the 28th.
Grocery stores and pharmacies are more likely to be open on Turkey Day, though hours may vary by location.
BlackFriday.com has a list of large chain retailers that will be closed on Thanksgiving. My Central Jersey has a breakdown more tailored to, well, Central Jersey.