Common etiquette in Japan is to not bring any food or beverages from outside into an establishment that serves food or drink for reasons of food hygiene management and so that people can enjoy the restaurant's own offerings. Some restaurants may display a "No Outside Food or Drink" sign, but whether or not you see a sign, please follow this etiquette. If you wish to bring your own food or drinks, please check with the restaurant staff in advance. It is also not socially acceptable to enter a restaurant while munching on a snack or something purchased elsewhere, including takeout food.
Food court rules may differ from restaurants, so you might want to check the rules for a particular food court regarding outside food and drink.