The shopping is very good in Las Vegas, there are some out of town retail parks that sell cheap trainers and things like that if you can find them. North and South retail parks I think? There was also a shop somewhere selling cheap pairs of converse, but I can't remember where. Otherwise there are really great American stores like Sephora for cosmetics, Victoria's Secret, American Apparel, Abercrombie, Forever 21 etc.
No-one has yet mentioned the Bellagio's breakfast buffet, it's immense and delicious, but it is about $25 a head so if you go, make sure everyone is hungry to make the most of it. The fountain show there is lovely as well. We saw Cirque du Soleil's "O" show at the Bellagio too, and really enjoyed that.
For a really great meal try Carson Kitchen in the north of the town not far from down town. If we went back, I would spend every evening down town at Fremont Street, it feels like the authentic Las Vegas. You will recognise all the buildings from old movies and the place really has a pulse at night. Lots going on including live music and street concerts, a great big digital ceiling and zip lines. We loved it but only discovered in on our last night. Can't comment on how it is during the day. We did get a taxi there and back from the strip.
We did do a lot of walking despite the heat (in June) and it was like an oven. There are misters everywhere and you can duck in and out of hotels to cool down before you go out again. If you are walking on the street in the evening, you might see the odd cockroach, so be prepared for that, it's a bit startling if you have never seen them before.
We loved the Grand Canyon, but we didn't go from Vegas. We took a train from a little 'Wild West' town on Route 66 called Williams. That was a bit different and a lot of fun as they put on a bit of a show before you go and the train gets held up by highway men on horseback. It was good fun, and the canyon itself was very impressive. Some of the native american art and jewellry you can get the in the area is lovely if you want a nice keepsake, but its pretty expensive too.