I'm in the military and I use Navy Federal Credit Union for my bank. Do I file the interest as my home state, the state I work in, or the state the bank is based out of?

If you have some reason to have to list it for some state....it is only taxable by your HOR state....or SLR (state of legal residence....if you changed it legally at some time during your service).   Where you are posted is immaterial.