You might consider the Hermit Trail in the Grand Canyon if you can get a permit. This trail takes you to Hermit Camp; about a good day's walk. You can then spend a day walking down to the river at Hermit Rapids and back and then another day hiking back to the rim. The trail is not maintained and is strenuous in places but is, in my opinion, much more scenic than is the Bright Angel Trail.
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May I walk in beauty.