You've already received a lot of good answers so let me just toss this in for perspective: there are camping trips and there are "destination" trips.
If you want to take a camping trip, plan on driving a distance that is short enough that the majority of the trip will be actually camping rather than driving. Three weeks is a great amount of time to go out around 500 miles and stay at two or three different campgrounds.
If you want to take a destination trip, the goal is to get there, do what you went to do, and come home. If the distance is great, then leave the camper at home, hop in the car and do some long distance driving to get there.
Generally speaking the advantage of having the camper while you are "there" isn't great enough to make it worthwhile hauling the camper across the country.
Now, if we're talking about a popup camper or a teardrop or a campervan. combining the two starts to make more sense.
