Doing a grill-out at a remote park is a LOT of work. It's important to move as much prep work as possible to the day before, and as much of the cleanup as possible to the day afterwards.
Work that can be moved to the day before:
Buy food, and start marinating it.
Pack the bags, and pack the car.
Work that can be moved to the day after:
Unpack the car.
Do the second more thorough grill cleaning (the one that's done at home, to get it ready to sit on a shelf for weeks).
notes
I was surprised that most big parties arrive early and monopolize all nearby picnic tables. It can be good to either arrive earlier than we really need to, or to bring your own table and chairs.
The second cleaning (at home, the more thorough cleaning so it can sit on the shelf for weeks/months):
Using dry tools (either a bristle brush or paper towels) remove as much of the stuck-on ash as possible.
Put the grill in the bathtub, and use a bucket of soap and water to clean it. (with no water drawn in the tub, it's only used to contain the mess) Things that can help this job:
a sturdy bristle brush that's soft enough to not scratch the paint
dish gloves (even just because the grates are a bit sharp)
a dish rag
scour pad / scour sponge (But only on grates! Don't use abrasives on the nicer painted parts.)
For when there are things really stuck onto the grates: