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Not quite 10K but close :) and you got the idea. I will write about it as soon as I find time.

Thing is though, most people in Grand Canyon concentrate on the South Rim. Even if that, like you mentioned, close to the visitor center. Even on the south rim if you travel a bit away from the popular points on the rim trail, it's easy to find solitude. North rim is far less crowded, further away from the main highways. And from either rims if you just walk a mile down you can virtually have the whole canyon to yourself.

But that said it's no outback when you can order a pizza and beer while you read a book. Still there is a magic that can be felt as the crowd leaves by sunset. Moonlight or during new moon, you don't need a flashlight it's so bright! It's is told that you can read a book by the light of Venus! I haven't tried it though! But I can tell you its pretty bright.

I'd want to feel the solitude, to get lost in the beauty of the natural wonder that the GC is so it'd be the north rim for me. Having said that, I think it'd be cool to sit around with your family and order pizzas, share a beer and tell lies. Also, reading a book by the light of Venus? Yep, I want to do that!