I've hiked the South Lykken trail in Palm Springs a million times since moving to Palm Springs 18 years ago. I've always started the hike at the S. Palm Canyon Drive trailhead and hiked up for about 30 minutes and then back down. Consequently, I only saw a small part of the trail and a experienced a certain view of the city. I knew the trail went much further and eventully came back down at another trailhead in the North. I didn't know where that was. I stumbled upon it over the weekend and check it out. The North trailhead is at the end of Mesquite Ave. It's another amazing hike and features a completely different view of the city. I think it's a nicer view. In addition to the city views, you also look down upon TahquitzCanyon.
The South Lykken trail from the Mesquite Ave trailhead is a great intermediate hike containing a few steep, but mostly moderately inclined switchbacks. Toward the top I found a "park" called the Josie Johnson Vista Park. Park is in quotes because it ain't much more than a few wooden picnic tables surrounded by cacti, rock structures and mountains. Having written that, if you like to hike and like to eat, I think it's a great place to take a lunch break with friends and family.
To get to the trailhead, take Palm Canyon Drive to Mesquite Ave and head West on Mesquite towards the mountain and towards Tahquitz Canyon. You can park on Mesquite before Belardo. It's a great hike and you should really check it out.