First thing you want to do is file a change of address with the Center your application is at.
As for getting your case transferred, I am fairly sure its not dependent on where you live rather where the company that you work for is headquartered so check on that first.
Also, if you are in the I-485 stage and are using AC21 to change jobs (which is why you may be moving) then you will need to send an employment letter and pay stubs informing INS of the change. This may prompt INS to transfer the case on their own accord.
I have not heard of anyone getting their case transferred to another center upon request. Transfers have been done by the officers themselves for whatever random reasonings they may have.
Hopefully someone who has gone through this before can give you a little more definitive information.