In my experience, being upfront and honest about the situation is best. I do not think that many people would unfairly judge or punish you because you'd like to work at a school closer to home. If you approach the Asst. Principal over you with that information as a professional courtesy, they can at least know that they may need to fill your position whereas they may not have been looking at anyone with your subject/content area, etc. I think that they would be grateful, not spiteful. I did not move out of district, but I did leave one school for another for the same reason and I followed the above advice. They were actually incredibly supportive and helped me get the interview/job at the new school.

If you know you are not going to return to your district then don't sign the contract. Tell your administrator exactly why you are looking at other jobs. If you plan on returning to your school if you can't find another job I would ask your administrator whether or not you should sign the contract. Many times it is up to the principal to decide if you can be let out of your contract. The sooner you give them a heads up the better. They can at least be on the look out for potential replacements if you do leave.

I would be one hundred percent honest with my principal about leaving. Even though it may be nerve racking I am sure that they would understand that you would want to work closer to your home.

Just be honest and straight up to the administrators. Tell them the truth that you love your job at the school but you feel as though working closer to home will be more beneficial. Also make sure the school have extra staff or teachers that are great candidates to take your position.