I'm a big hiker, so...
Lived in Vegas for 4 years. I always recommended Red Rocks. Its only 30 minutes west of the strip and it is amazing for quick little day hikes, especially when its not 110 outside.
Also, Id suggest driving up to Mt. Charleston, another beautiful area. Pines and snow within 45 minutes of the strip. Hike the Bristlecone Trail.
Would also recommend driving the Lake Mead road from Lake Las Vegas up to Overton/Valley of Fire before driving back into town on I-15. Great little road trip.
My favorite hike is Arrow Canyon just north of Moapa only a short trip north on I-15. Google it. Awesome slot canyon. You will likely have it all to yourself, as I've only seen other people on the weekends. Petroglyphs and and a mile long canyon that varies from 8' to 100' wide. Amazing place.