The Saguaro is one of the largest cactus in the U.S...
saguaro
I you fly into Phoenix Arizona you may want to visit Tonto National Monument.
Tonto National Monument - Directions (U.S. National Park Service)
Going to a desert museum is a great way to see the flora and fauna of the desert in a rather small area.
Also in Arizona is the Arizona-Sonora desert museum.
Arizona-Sonora Desert Museum
Closer to LA is a very nice desert to visit called Anza-Borrego. I’m not sure if there is anyplace to stay in Anza Borrego, I just camped out in the desert when I was there about 15 years ago.
Anza-Borrego Desert SP
Other large cactus are Joshua Trees. This National park is not very far from L.A.
Joshua Tree National Park - index (U.S. National Park Service)
Hope you enjoy your visit to the south west.