You could do a grilled pizza, but take it breakfasty with some sausage or bacon and eggs. Cheese of course.
Slip a fry pan on the grill and fry what you want while you toast bagels, english muffins on the grill. A flame kissed benedict with maybe a fried soft yolk egg would be good. Toast the muffin and canadian bacon on the grill.
Precook some waffles, then toast them to crispy pefection on the grill.
Sausages, both link and patty shapes.
Use a pastry shell or a stiffish sweet cake base and make a grilled fruit tart. Toast the cake base as well as the fruits with sweet rub. Bind it with a thick creme anglaise perhaps. The tart shell Hubert Keller makes here would do the job. http://www.hubertkeller.com/recipes/mod/recipe_316tartauxFruits.html
I could see the appeal in offering a lightly smoked strata even, but you might not have equipment or time for that to cook.