Something like this should work:
First, create an RNG (for random number generation) and get access to the screen size:
onready var rng = RandomNumberGenerator.new()
onready var screenSize = get_viewport().get_visible_rect().size
Next, randomize the RNG to ensure that you get truly random numbers:
func _ready():
rng.randomize()
Finally, in your existing mouse_entered
event handler, create a new random position for the Area2D
node:
func _on_Area2D_mouse_entered():
var new_x = rng.randi_range(0, screenSize.x)
var new_y = rng.randi_range(0, screenSize.y)
$Area2D.position = Vector2(new_x, new_y)
With that, each time you enter the Area2D
it should move to a different, random screen position.