Sorry. The last day made no sense to you - because you live there and know the area. It was a simple way of saying we will return to where we started from - to get to our rental vehicle and drive to our next venue.
EDIT: I just read your trip idea again and I think the confusion is you're talking about the North Kaibab when you mean the South Kaibab.
So you're thinking about:
Day 1 - sleep somewhere at the SOUTH rim - Mather campground, great
Day 2 - Hiking North Kaibab (you mean South Kaibab down to the Colorado THEN the North Kaibab) to Cottonwood Campground -OK
Day 3 - Hike from Cottonwood Campground [BACK] to Bright Angel Campground
Day 4 - Hike up to the top [South Rim] via South Kaibab Trail (sleep somewhere at the top - preferrably in a tent) No, I'd go up the Bright Angel Trail, lots of reasons, mostly you get water that way.
Day 5 - Hike to North Kaibab Trailhead No, take a short shuttle bus at the start, so you wind up AT your car on day 4.
I like the similar trip I described at the bottom of my post better, stopping at Bright Angel camp on the way in and at Indian Garden on the way back up.
EDIT: Ignore down to ****; I misunderstood.
You're describing doing a rim-to-rim-to-rim in four hiking days, in June, starting at the North Rim. Probably more ambitious than most, but reasonable; lots of people do it. It's just that you plotted out a fairly conservative trip for the first three days and then all of a sudden on the fourth you're doing a rim to rim, half of the entire trip. Again, lots of people do that in June but it's a LOT more than average. I would take the same total length for the trip and break it down so you're not doing so much on the last day.
Example (and again, starting form the North seems strange, but if that's what you want):
1. Sleep at North Rim as you describe.
2. Down to canyon floor, across to BA
3. Up to the South Rim via BA Trail
4. Down to BA via S Kaibab Trail
5. Across canyon floor and back to North Rim
It's not a trip I would do in June, but there you are.
**** This is the trip I'd suggest:
As a first trip in your timeframe I'd start from the South Rim, go down S Kaibab but only as far as Cottonwood, see some sights leisurely, then return to BA an up the BA Trail.
Example:
1. Sleep at South Rim (Mather campground is great).
2. Down S Kaibab Trail to BA campground. You should have a few hours to explore.
3. To Cottonwood campsite, spending a couple of hours at Ribbons Falls.
4. Back past BA camp and up BA Trail to Indian Garden camp, visiting Plateau Point for sunset
5. Continue on BA Trail back up to South Rim
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