Another possibiolity to consider would be to go to Grand Canyon, then continue on to either Monument Valley or (better for someone coming from/returning to Las Vegas), Lake Powell and Zion.
Go to either the north or south rim of the Grand Canyon (I'd suggest the north in your case), then continue on to Lake Powell and return via Zion-- (or do this in the opposite direction).
Head north on I-15 as far as St. George, Utah, then turn off and head east on Utah
State Hwy 9. At Hurricane, take the south road (Utah State Hwy 59 to the north rim of the Grand Canyon, then return via the north road (Utah State Hwy 9) that comes back into Hurricane through Zion. The rest of the route to take is as follows:
(1) Utah State Hwy 59 will become Arizona State Highway 389 once you cross the state line.
(2) Stay on this road to Fredonia.
(3) At that point, get on US Highway 89S (89 South) heading south. Get off on Arizona State Hwy 67, and go to the Grand Canyon. (Note that this road is closed from November to April, so go to the south rim during this time instead)
(4) Return on Arizona State Hwy 67 back to US Highway 89S, and go south once again until you get to US Highway 89N (89 North).
(5) At this point head the opposite direction (north) on this highway up to Page, Arizona and Lake Powell.
(6) Head west (north) on US Highway 89N to Kanab where 89N merges with 89S and becomes just 89.
(7) Go about 10 miles on US Highway to Mt. Carmel, Utah, where you will get on Utah State Highway 9 going west.
(8) Go through Zion National Park on this highway, coming out at Hurricane, and then back to St. George, Utah
(9) Take I-15 back to Las Vegas, Nevada.
I'd say you could do this in 3 days (1 day Las Vegas to the Grand Canyon), 1 day over to Page, Arizona or the Lake Powell Resort, and then 1 day back to Las Vegas (this will be the longest day's drive).
If, on the other hand, you just want to see other stuff close-by to Las Vegas, consider the Red Rocks area or a day drive out to the Death Valley and back (a full-day's trip).
Take water no matter where you go. This is the desert, after all--and book ahead--especially for the north rim--which fills up months in advance. go to the nps.gov website for this.
Enjoy