Is there a friend or relative that can pop in and check on your hamster while you are away/take your hamster in for the length of your vacation? This is the best option as it will avoid the undue stress of traveling and the possibility of your hamster overfeeding on the food left for it and then running out. If this is not possible then you are left with your two suggestions, neither of which is ideal. I would not recommend leaving a hamster on its own for longer than three days so if these are your only alternatives then I would take him with you.

Make sure you take a cover for the cage while in the car and don’t place it near the air vents, an open window or in direct sunlight. As long as the temperature in the car isn’t likely to fluctuate then I would leave him in the car when getting gas etc. Things will move around a bit in the car even with the best driving so don’t put anything in the cage that could harm your hamster. For example, use a water bottle and scatter a little bit of food around the floor rather than water/food bowls. A quiet background level of music will be fine but your hamster will probably be trying to sleep so wont appreciate anything very loud.