Thanks everyone for all your input. They have been invaluable. I
finished snaking the wire through the exterior wall from the inside
outlet. I did this by creating an interior opening right where I had
the exterior hole so that I can use this opening to push the wire
through the exterior hole. This helps me to minimize the size of the
exterior hole. I will cover up the interior opening using a blank
cover. Should I use drywall patch compound to patch up the interior
opening first before installing a blank cover? The opening is about
2.5" x 2".

Now I just need to go and purchase an outdoor outlet box with GFI
outlets and attach it to the stucco wall. How do I screw the outlet
box to stucco? Are there special screws that I need to use? Should I
use plastic wall anchors?

Thanks