There is a trail all along the edge of the south rim. You will see the canyon from many different vantage points. Be sure to look for the CA Condors from the rim. I recommend at least a short walk down into the canyon. We took our kids who were much too short for the mules down this way. Bright Angel trail is probably the most popular, and it starts right on the rim where the hotels and restaurants are. There is a water and bathroom point at 1.5 miles. You can get a slight feel for the vastness of the canyon even by walking a little way into the beauty. Start EARLY, like 6 am or so and take a back pack with way more water than you ever think you'd drink. They say the walk will take twice as long back out as it does going down, but for us it only about 5 minutes more.
The NPS has electric buses which travel most of the south rim. From each pick up point, you can go back to the hotel, or a different point along the route. They have some express buses really early int he morning to some of the outlaying trail heads, like at 4 am, 5 am and maybe 6 am. These buses are always free.
If you can, dinner at El Tovar is wonderful. The Bright Angel Cafe was good for lunch, and I think we had dinner in there once also. If not staying at El Tovar, make sure you go in and see the lobby anyway.
Beware of the squirrels. Because so many people have fed them, they are no longer wary of humans. Even though there are signs and announcements everywhere, you'll still see people feeding them. Anyway, one of my kids was laying on a bench on the porch of El Tovar with an ice cream cone in hand. A squirrel jumped up onto his chest to get the cone. While the kids all thought it was absolutely hilarious, it scared me to death.
Take warm clothing. Even in July I was surprised at just how cold the nights were. It was down to the low 40's and that was the South rim. North rim is even colder.
Although the 2 rims are only 10 miles apart, I think the driving time is something like 7 hours.....definately not something you can sneak in easily.
Take binaculors.
There are no pools at the NPS hotels, in case you need to give your kids a heads up.
Free Ranger programs outdoors nightly on various topics.