In the fridge of course! :)
You can buy a fridge from the premium section in your decoration menu and place it in your cafe. Once you have it, you can tap on dishes that are on the counter and store them in the fridge. This helps keeping the dishes fresh and gives you extra space for preparing/serving more dishes!
You can also increase the capacity of your fridge to store more food! Currently the maximum storing capacity is 90000 servings.