My favorite place to visit in Las Vegas is a 13 mile driveable/bikeable/hikeable loop, just west of the strip. From the 15 or LA Blvd, take Charleston west and after crossing the 215 and getting into the hills, you'll be rewarded with a spectacular sight on your right side.
After paying the $5 entry fee, you can stop by the visitor's center to get an overview of the 195,819 acres and more than 30 miles of hiking trails. The loop road is studded with trailheads that either take you into the unique geologic features, box canyons, or even a children's trail with a cave at the end.
If you have a chance to leave the strip, I would highly recommend a side trip to visit Red Rocks. Plan on between 3-4 hours to get the most from the area.