During my search to try and find a new job in another city I thought about getting a P.O. Box.
The main reason I did Not get one was that seeing P.O. Box on your resume, to me, seems like a red flag. It makes it seem like you do not live in that city or that you move frequently. Or the company might not give it a second thought.
If you do get asked as to why you have a P.O. Box make sure you have an answer ready. If they ask you about the P.O. Box address they might ask where you are currently living. Do not make up an outrageous lie, they will be able to tell. If anything tell them that it is a temporary thing. They might not press beyond that but be prepared if they do.
Personally, if you are not living with in 2hrs of the city you are trying to get a job in or unless you were going to be living there in 1-2 months, I wouldn't bother. Most companies want to know what your plans are and when you will be in the city. They will not pay for your travel costs to interview with them and plane tickets add up fast. a P.O. Box would just be adding to the cost of your search
If you will be in your new city in 1-2 months put that on your cover letter. If you are planing to go there prior to look at apartments or houses add that you would be available on such and such days. It is much easier to re-schedule with your Realtor agent then a potential job.
Again, mention these things in your cover letter. Have questions & answers ready for any and all phone interviews. It's the little things that can make your search just that much less stressful.