Where can we park a camper for the night close to the steakhouse.

Their is parking directly behind the the Big Texan for big trucks, campers etc.

They have an RV park with limo service to the restaurant

Yes. There should be an RV park fairly close.

They have an RV park as part of the whole facility according to what I read while I was there

Thanks, just booked a spot at the RV park, really great rate.