Tiny Camera Recommendation

I find a need to place a very discreet camera to monitor the area around my front door. The door is in a walkway of sorts about 4 feet wide. Placing it in the door somehow would give a limited view but make battery changes and possibly even full time power easy. A longer view from one end of the walk would be ideal and would provide the perfect view but would be very difficult to change batteries especially in a covert way as it would be placed in a light fixture but an 8' ladder is needed to access it so discreet would be defeated. I can not modify the structure and have no access from the opposite side of the walkway and it has to be as concealed as possible. A tall order I know. Internet or cell phone connectivity ideal as access to a memory device would be the same as the battery.

I have a situation where there is some vandalism occurring and it would be nice to catch the perpetrators in the act - I already know who it is I am looking for proof. The long range view is better because mounted in the door only gives me a glimpse as they pass and likely just a shoulders/head but I can't figure another way.

Any ideas? Also any camera recommendations would be appreciated.