Yes, the co-signer probably should not have been so unwise as to sign on a car loan in the first place. And I understand you have to do what is best for your career and future. I guess my frustration is that I always tell people never, ever to co-sign -- even for a spouse. A co-signer gets very little benefit and 100 percent of the liability. Your situation is another example I will give as a cautionary tale.
My frustration is based on the fact that you signed on this car loan and agreed to pay. Now, you are moving and don't want to be bothered anymore. Too bad. You put another individual's credit and personal assets at risk. The lender was the only smart one here because it got someone else to sign on this car loan.
To be very clear, the co-signer is 100 percent liable for this vehicle. He or she will be sued by the lender within months of default. The lender will repossess the car, will sell it and then will sue the co-signer for the difference between the loan balance and sale price.
At this point, you do not have many options other than to continue making the monthly payment.
Contact the co-signer, and maybe he or she would be willing and can afford to take over the note while keeping the vehicle. I assume that might be a contentious conversation since you are basically saying you don't plan to honor your commitment.
Contact the lender to see whether you are able to sublease the vehicle. You might be able to find a third party willing to maintain the car and make the payments. I believe that would be a breach of the loan terms, but you don't have many other options. While the lender would prefer to receive monthly payments over the cost of collections, it is prepared for the latter.
Try selling the vehicle. You might be able to sell the vehicle for less than what it is worth and sign an unsecured note with the lender to pay the difference. The co-signer would have to agree and also be liable on the new note. I have seen this when dealing with small car lenders and not the big finance companies.
Try doing the responsible thing and honoring your commitments. Do everything possible to protect the co-signer and return the favor already granted to you.