The after Christmas sales are over, but January is known for being a time when particular categories of items go on sale.
White sales, also known as linen sales, where stores are marking sheets and towels down by 50%. Target has some good deals on sheet sets right now, including organic cotton sheets. I've always liked the Macy's sales with their king sized, deep pocket sheets for around $39. Remember that high thread count does not guarantee high quality. Feel the sheets; are they soft to the touch and dense, then they will be a comfortable, long lasting sheet.
The stores are unloading their winter clothing to get ready for the new Spring lines. Don't buy trendy items, but focus on well made classics that will serve your family for years.
Electronics are being marked down to lure in those pre-Superbowl buyers. May be a good time to purchase a new TV (if you watch TV).
Many people are doing a post holiday purge of their belongings, so the thrift stores should be filled with new items. Think ahead and buy your children winter clothing in next years, anticipated sizes (only if you have the storage space). But before you buy keep repeating to yourself, "Hand me downs are good. Hand me downs are good.", then decide if the younger children really need new or new used clothing.