One of the best things to leave in your old neighborhoods courtesy. Just because you are leaving the vicinity does not mean that you have to leave the good friends and more importantly the good manners that you have. Remember that it your primary duty to care for your house and whether you are selling it or renting it out, keeping things in good and its right and proper place is the best way to leave the place.
As much as possible put your house in its best shape. You may think that your house is not your responsibility anymore but you are so wrong. If you have the time, clean it up first before leaving. This will be as courtesy to the next occupant. Do unto others what you want others to do unto you. It follows that if you want to arrive at a clean house, you have to clean the house that you are leaving.