I would check out the Havasupai reservation, just west of the park. They have a lodge down in the canyon that can be reached by a relatively easy 10 mile hike (much easier than the trail into and out of Phantom Ranch). They’ll also take your bags down and up via mule, so you can just day hike. I’ve never been myself, but it is supposed to be quite beautiful down in that part of the canyon.
Inside the park, I’d recommend hiking as far down below the rim as fitness and weather allow. Some of the best parts of the trails are just below the rim.
If going in late spring or summer I recommend the North Rim. Better weather, nice lodge with dining room overlooking the canyon, and 1/10th the visitors… Bring your own wine though, slim pickin’s up there.
One thing I would highly recommend, and this goes for most all of our National Parks: take full advantage of ranger led programs – lectures, hikes, etc. These are your tax and entrance fee dollars hard at work. Some of the best experiences I’ve had in our parks were with these programs (Canada does a great job as well).
2 years ago we did the heli tour from Vegas for the day. Fun trip. Heli over the hoover dam and lake Mead, head towards the canyon and pass by the glass walkway, then land at the floor for lunch. Speent an hour down there then back up and back to vegas. Awesome experience and a great way to see the canyon from above and below. Would do it again in a second.
That’s about the perfect time to go to the bottom. One day down, stay overnight at the Phantom Ranch (if you can get a reservation) and back up the next day. Best way to experience it. They will talk you out of going to the bottom and back in the same day but it can be done depending on the weather. The weather is something to be feared in the canyon. People do die. Bring water and a camera…