Why do I hear a clicking nose coming from my dash when I start the car.

Could be a HVAC door actuator. These doors control air flow to your vents, floor, defrost etc and the gears are made of plastic and over time break or strip or get stuck. The clicking is the actuator motor trying to open or close the door and the gear slips a tooth and you hear the "click" and will do it several times before it gives up. It should stop some seconds after you start it. You can try this, with the engine running, turn of the ac system and leave it off. Then turn off the engine. With the ac system still OFF, start the engine, if the clicking is gone then its an actuator.