What everyone else said, all great suggestions. Keep in mind, though, if you're pressed for time (and with gas around $3.50/gallon!), you don't have to drive all the way to Zion, Death Valley or Whitney to get in some good hiking.
Just a little south of Vegas going toward Hoover Dam/Lake Mead, Bootleg Canyon in Boulder City has some nice hiking as well as mtn. biking, as Drew mentioned. I was there a few weeks ago and, while climbing Black Mtn., encountered a herd of 28 (I counted) bighorn sheep, the Vegas skyline looming in the distance -- pretty cool.
The Spring Mtns. (west of the city) are nice as is Red Rock Canyon, a must if you've never been there. Turtlehead Peak, a bit higher than Mt. Washington, is the must-do summit.
Mt. Charleston, almost 12,000 ft. in elevation, has some great trails!
Valley of Fire State Park isn't too far from the city and is the place to go if you're into rocks (think Joshua Tree) and petroglyphs. Fun scrambling.
Finally, don't discount Vegas. Yeah, it's disgusting on some levels, but the people watching is fun, and you can't beat a 2 1/2 foot long frozen margarita. I also admit to sort of liking the Bellagio's water show.