I started to create a post of where one can find a good selection of gluten free / dairy free products but then decide it would make a better list page: Gluten Free / Dairy Free Stores in NJ . I've tried to list out the brands you can find in each of these but keep in mind that inventories change and for the chains, not every location will carry the exact same products. I will update this list as I encounter more stores.
I have listed the independent shops first. Sadly, they can not match the economies of scale the major chains have and therefore tend to have higher prices. However, you are more like to find obscure products, upstart companies, and new products in these locations.
If you know of any shops I am missing please mention them in the comments below.