Turtlehead Peak (elevation 6,323 feet) is an excellent short hike with great views from the summit. The peak is located in Red Rocks Park, just a few miles west of Las Vegas. The distinctive turtlehead shape is visible from many places in the city, but it doesn't really appear prominent until you get up closer to it. I did this hike on New Year's Day and again on Jan. 4th, 2004. The normal $5 entrance fee to the Park was waived on New Year's Day.
The official description of this hike from the BLM is "5-mile round trip, very strenuous". The hike has a 2,003 foot vertical gain from the trailhead elevation of 4,320 ft. The ascent took me exactly 1 hr-15 min both times. The trail takes a fairly direct route from the Sandstone Quarry trailhead up a gully to the west of the peak. Near the top of the gully, the trail gets pretty steep, and becomes indistinct and braided, with several possible tracks. You'll probably be grabbing on to boulders or outcroppings in some places. Just don't get too high on the side slopes and you'll be OK. The fragile desert vegetation is starting to show some wear and tear from hikers wandering off the trails, so try to stay on the established tracks. And remember that some of the plants up there can bite back.
The sun doesn't hit the upper gully until late morning, so be prepared for the cold if you're doing this hike in the winter, especially if it's windy. My thermometer read 25-degrees just below the ridge at 8:15 AM on Jan. 4th. After you reach the ridge to the summit, you'll be on the shady (north) side of the mountain for the rest of the hike, and this section of the trail can become very slippery with ice and packed snow during the winter months. The descent can be especially treacherous if you don't take it slow and steady over the icy patches. You might even want to take along a pair of instep crampons if you have them handy.
Once on the summit, make sure to walk a few hundred feet to the east (toward Las Vegas), and check out the view of the fantastic multi-colored rock formations near Calico Basin directly below you. This is also a great place to get a birds-eye view of the peaks of the Escarpment (Wilson, Rainbow, Bridge, etc) and the canyons in between them. Snow-covered Charleston Peak is also visible to the northwest. The Turtlehead summit would offer spectacular views of the Las Vegas lights, but that might pose a logistical problem, as the park gates close at night. Anyway, this is probably not a descent you'd want to attempt after dark. If you start first thing in the morning, it might be possible to reach the summit in time to watch the sunrise over the desert.
On the way down from the peak, I'd suggest you make a short side trip out to the little secondary peak (clearly shown on the Topozone map) at about elevation 5,930 feet. Instead of turning left on the trail down the gully, continue straight out the ridge to the northwest. The view looking back at Turtlehead from this secondary peak is quite impressive. You should then retrace your steps to the main trail, and descend the same way you came up. Keep in mind that the road through the park is a 13-mile, one-way loop, so when you finish the hike you still have to drive all the way around the loop to get back to the highway.