Been there a few times and loved it each time.
The colours are amazing.
Red Rock Canyon is closer. I have been there many times, and always enjoy the lovely scenery.
Done a couple of hikes there, and seen a few wild animals over the years.
Mount Charleston is always a nice place to visit.
Its around 20 degrees cooler than Vegas, so worth going when its to hot elsewhere.
A few nice trails to hike too.
First hike I did up there was the Mary Jane trail.
Only a six mile round trip, and good for beginners.
Also worth driving around to see some of the beautiful houses around the area.
This past December I went hiking over at Spring Valley Ranch State Park, which is around 15 miles west of Vegas.
Some nice scenery to see there.
Lake Mead is always worth a visit if you like water.
Nothing better than splashing around on a jet-ski with the sun blazing down and the water spraying your face as you zoom along at 40mph.
Lots of fish and a few feathered friends to see along the way.
you can also get close to the rear of the Hoover dam.
Closer to home you can visit the Flamingo wildlife habitat.
Its free and has a load of wonderful creatures to see such as Flamingo's, Koi, Turtles and many many more.
At the Mirage you can visit the Secret Gardens and see Tigers, Lions etc, and see the beautiful Dolphins swimming around. They perform every so often when the trainers ask them to.
Worth the admission of under 20 bucks, IMO.
Over at the Bellagio the amazing Conservatory is worth a visit.
Its only a 15 minute thing, but its free and always a delight.
If you want to travel further afield other places I have visited while in Vegas, and loved are Bryce Canyon, Zion National Park, Yosemite and of course the Grand Canyon.
All of those are day trip though, so probably not what your wanting.
Enjoy whatever you decide to do.
There is much more to Vegas than gambling, drinking and sex. (Although those three things aint to bad, are they...LOL.)
VOF photo below. Look at those amazing colours