Joshua Tree National Park is a special place where the Mojave desert and Colorado desert ecosystems merge together. Joshua trees (actually yucca plants) are native to the Mojave and are slow growing. Night time is a great time to visit for star gazing, as the park in a Dark Sky Park.
There are many short hikes throughout the park, but be aware that pets are not allowed in the park, except on the Oasis of Mara, which is a paved trail. Make sure you have plenty of water and take some snacks with you, no matter what time of year you visit.