These type of cookies tend to dry out quickly. So, I would recommend that they be stored in an airtight container. Place the cookies between sheets of waxed paper to keep them from sticking together. The cookies can be stored about a week out of the refrigerator, if they last that long. If you don't think they will be eaten quickly store them by the dozen in the freezer.
The link below has some tips from Betty Crocker on storing cookies.
Cookie Storage Tips