I love Vegas, but don't gamble, so I always have to find other stuff to keep me occupied. My favorite place to go in Vegas is Red Rock Canyon. It's only about a 20 minute drive from the strip. There are all kinds of places to stop and take photos or go for a hike. I usually take a picnic lunch and just sit and enjoy the view. Mount Charleston and The Valley of Fire are also wonderful places to get out in nature, but they are a bit farther away. The Hoover Dam is also pretty interesting, but usually very crowded. Lake Mead is also makes for a nice afternoon, but is a bit chilly this time of year to go out for a swim or to go fishing.
I really enjoyed the Atomic Testing Museum, the Mob Museum, and The Neon Museum and Boneyard. As for shows, my absolute favorite is Jubilee at Bally's. It is the only old-Vegas style show that is still in production, and I believe the showgirls still wear the original costumes from the 1950's. Every one I have ever taken to Vegas has told me it was the highlight of their trip. Also, pretty much anything Cirque is a sure bet to awe.
For fun, free stuff to see, there's The Fall of Atlantis at Ceasar's (way in the back of the shops), The Palazzo Waterfall Atrium, The fountains at the Bellagio, and The Fremont Street Experience, especially if you happen to catch the "American Pie" Showing.
If you are going to the Grand Canyon, I recommend a little detour to the Grand Canyon Caverns in Peach Springs Arizona. It is just one of those quirky roadside attractions along Route 66 (Mile Marker 51, if I remember right). There are so many random things going on at that place that you just have to shake your head and go with it. The tour of the caverns that go under the Grand Canyon, and the cars in random places like from the animated movie "Cars" alone are worth the drive. They offer horseback riding and miniature golf, a decent campground, and being in the middle of nowhere, its an amazing place to go star gazing. Each time I go there, I discover something new.