If you move to another state, you will need to apply for a LVN or LPN (that's what they're called outside of CA and TX) license by endorsement in that state. You do NOT need to retake the NCLEX-PN. However, you do need to meet whatever requirements that the new state has for licensure.
You can apply for another state's license before you move there--I highly recommend you do this because then you can start searching for jobs before you move, and you can start working as soon as you arrive. If you decide to move first and then get the license, then you have to get licensed right away after you settle in the new state, usually within 30 days.
You get to keep your CA license until it expires. Actually, you can continue to maintain your CA license as long as you meet the BVNPT's renewal requirements (you have enough CEUs, etc.) and you're willing to fork over the money for renewal fees.