We are going to Vegas. The proper Grand Canyon parks are too far from the city of Las Vegas but is there something within 3 hours that provides a view of the Grand Canyons and is popular?
As you've probably already discovered, the normal place to visit the Grand Canyon when coming from Las Vegas is the "South Rim", which is about 4 1/2 hours drive (each way!) from Vegas.
Although the Grand Canyon (and the Grand Canyon National Park) does extend almost 100 miles further west of the "South Rim", there are no suitable roads that allow access to the canyon within that area.
There are a few roads that will get you within walking distance of the Canyon, such as the Hualapai Hilltop Highway, as long as your idea of "walking distance" is 10+ miles each way :)
If your time is limited to 3 hours your only option is to take one of the many helicopter tours that leave from Las Vegas, although obviously that'll cost a lot more than driving. There are also several bus trips, but they will obviously take longer than driving yourself.