Every campground I've ever been to has had either charcoal grills or firepits with grates for grilling. All you need to pack is charcoal, lighter fluid and a match. Incidentally, you can put a regular kitchen griddle or cast iron skillet over any campfire; the fuel source is irrelevant.

Pepsi can stoves work really well and are easy to make (do a Google search for plans). Fuel is cheap, available everywhere and the amount of fuel in your bottle is never a mystery like it is with propane. If you decide to try backpacking, you'll be all set. It's also important to note that if you ever fly to your camping destination, you'll need a brand new, in the box stove. A Pepsi can stove is great for this because you just make a new one for the trip and toss it in the recycle bin when you're ready to go home. Just make sure to use a wind screen, otherwise you'll run through a ton of fuel.

We have a 1-burner Coleman left over from our car camping days and I haven't touched it in years. Even on the lowest setting it burns way too hot (so food gets scorched on the bottom and stays raw on the top) and there's no way to adjust the height of the pan over the stove.