Substitute Swiss, Edam or Gouda cheese. Each has a nutty flavor that is excellent when heated. Croque monsieur, the French version of grilled cheese, consists of ham and cheese. Croque madame uses chicken and cheese. Give up the squishy white bread.
Rye bread is great when grilled.
It has an earthy aroma and full flavor. Egg bread tastes even sweeter in a grilled cheese sandwich and a robust sourdough bread is sturdy enough for anything you can pack inside. It's unexpected, but excellent. Fruit adds moisture to a sandwich. It complements most cheeses and ham products.