Hi Wardsgirl,
Joshua Tree is nice. We chose the Lost Horse Mine hike over Ryan Mountain, since it was a longer hike and a loop. The highlights were a bald 360 degree summit, the mine itself and tons of Joshua Trees on the descent (we went clockwise).
Our favorite place to hike is the Indian Canyons, just south of Palm Springs. It features massive fan palm oases, fast running creeks and spectacular views of the San Jacinto and Santa Rosa Mountains.
For easy hikes, I recommend the Murray Canyon/Coffman/West Fork Trail loop. Murray Creek is the largest of the creeks. You can continue beyond the main trail and take a path to the Seven Sisters Waterfalls. We got close to the falls, but turned around when my wife fell into the creek during a crossing.
Another nice and easy hike is the Palm Canyon/Victor trail loop. It is a bit more crowded, though.
For a longer hike, we LOVED the Maynard Mine Trail. It is about a 6.5-7 mile RT. It climbs up to a ridge and then downhill a bit to the mine. the views are amazing, especially after you get up and over the ridge, as you are right at the base of the snowcapped San Jacinto Mountains. Murray Canyon is right below you and there is a loud roar from the stream. You eventually come to a plaque for the mine and have to scramble to the right downhill to get to the mine itself, which is very impressive.
Please note that there is an $8.00 per person entry fee and the owners (Agua Caliente Band of Cahuilla Indians) give you a trail map at the entrance. You will find lots of tourists, but if you get a ways from from the parking lots, the crowds dissipate.
We are heading back to the area in March.
Have fun!
Marty