The bell tower of The Basilica of Santa Maria is, I think, the highest point in Elche. You can see everything, from the sea to the palm grove.
Climbing the 170 steps to the top allows you to really grasp the sheer size of the palm grove: it's like a green blanket that covers large areas of Elche.
The climb also has a couple of stops where you can see exhibitions of local culture. Do make sure to pay attention to the opening hours, though.