Parboil them, slice while hot and pour pickle juice or mild vinegar (like rice vinegar) over them. Allow them to cool and add oil and whatever spice combination you like. Mine is sea salt, onion and garlic powder, black pepper, paprika, cayenne. Shiitake mushrooms are good grilled.
Flatbread. I like to add seeds to the dough: fennel, dill, sesame, black pepper, serve warm with hummus or a spread of some kind. Potato flatbread is excellent with smoked salmon spread. Grilled pizza is popular, but it seems stressful to have to quickly put on the toppings and maneuver them off the grill. A round of camembert covered in pesto warmed on the grill with French bread and a plate of tomatoes just seems easier -- or split the bread and put everything in, wrap in foil, throw on grill.
Homemade flour tortillas. Much cheaper to make than buy. Grill and fill with grilled vegetables, meat or seafood, or make quesadillas. That Mexican hot flaming cheese dish with tortilla chips for starters, like deconstructed nachos.
Squid marinated in olive oil, white wine, lemon, fresh basil. Clams steamed in white wine and butter, herbs -- warm bread to dip in juices. Grilled oysters. Brining shrimp for 30 minutes in salt/sugar/water brine keeps them from drying out while grilling (keep shell on).
I mostly prefer dry brining, especially salmon. Sea salt and brown sugar, rinse, dry uncovered in the fridge until it is dry -- it will absorb smoke better and stay moist. My favorite wet brine is apple cider or juice -- add salt,rosemary, black pepper, mustard, bay leaves. A BBQ sauce can be made by reducing apple cider/juice, then adding cider vinegar, salt and flavorings. I'll often smoke apple-brined chicken wings before grilling (stovetop smoking in a wok which doesn't cook them all the way). One thing about dry brining meat is the 45 minute rule. That's the minimum amount of time for the brine to work. If you salt and season pork or beef and grill it fifteen minutes later, it's going to be tough. Either season immediately before cooking, or wait 45 minutes.
Popcorn.
Baked apples in coals -- I've wanted to try this for a long time and September is the perfect month.
If I lived somewhere I could have a grill, I think I would grill EVERYTHING.