Grand Maris has a small city owned RV park.. Technically you are not "Right on the water" you are perhaps 25 feet up and 100 feet from teh shore with a stairway down to the beach.
You might try one of the map services and look it up, Small town so just the name will be enough to zero in on it. Nice little town.
And not the lake but Michigan's best known water fall is Tahquamenon Falls There is a state park, and you are within walking distance of the river,, The RV park is lower falls, UPPER falls you you are a LONG walk from the falls (About a quarter mile from the parking lot to the waterfalls) Lovely golden falls. Highly recommended. Unlike the larger Niagra falls there is no commercical intrusion on the falls save for the canoe livery
Home is where I park it!