This is one of my favorite hikes to do early in the season. It's the most scenic route to Griffith Peak and there's no crowds like the South Loop trail. Snow melts sooner on this route than the other routes to Griffith Peak, but there can be snow making for some great photos. Griffith Peak has the best views of any summit in Charleston. You can even see Red Rock Peaks.
Griffith Peak is one of the major peaks in Mt. Charleston and stands just over 11,000 feet. It's the best choice for your first "high" peak in Charleston. It's not as high as Charleston Peak and does not have a scree slope like Mummy Mountain.
Here are the stats:
Distance: 10 miles round trip
Elevation gain: ~2,500 feet
Difficulty: 3 out of 5
Note: You do need a high clearance vehicle to drive to the trailhead.
Tip: Do this hike now before the Monsoon season starts.