Take the tour buses out to the end of the Canyon, and then get off anywhere on the way back for a good walk of whatever distance feels good to you. You'll see lots of birds, hear animal noises, and even smell bears (or maybe cougars). There are lots of people around so you can feel safe on the main road, and lots of trails leading off into more remote areas. The Federal Forest Service does a great job with the information center. Be aware, though: wear a hat, good walking/hiking shoes, bring water - even if you're only sitting on the tour bus - you'll be outdoors and it gets hot.
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