Zion Canyon NP is only 2.5 hrs north of Vegas and IMHO is a better day trip. At the Grand Canyon you're on the top looking down. At Zion you're in the bottom of the canyon looking up. Weather is usually better this time of year. Did the Vegas - Zion run this week. Another option even closer to Vegas is the Red Rock Canyon NSA about 30 minutes from the strip. I know neither Zion or Red Rock are "The Grand Canyon" but both are eqully beautiful in their own way and much closer.

Just my $0.02 worth