Usually, they're fair, IF the insurance adjuster who looks at your car is from YOUR insurance company. If it's the other guy's insurance adjuster, he might try to low-ball you. You DON'T have to accept it.
If the damage is only cosmetic and your car is drivable, then take your insurance company's check and get your car repaired AFTER you move. Of course, the repairs might cost more at a repair shop in your new town, but that's a chance you'll have to take, if you wait to have it repaired.
If your car is financed, you have no choice - you HAVE to have it repaired somewhere. The check you receive from your insurance company will be made payable to you and the repair shop where you got the estimate you submitted.