There is, of course, no objectively correct answer to this question. The answer depends very strongly on such things as one’s beliefs about the dangers of oil drilling, one’s attitudes towards the environment, and one’s conclusions about the need for domestic sources of energy.
First of all, answers to this can vary based on people’s perceptions of how safe oil drilling is. People who remember the Exxon Valdez spill in Alaska and the Deepwater Horizon disaster in the Gulf of Mexico will tend to feel that oil drilling is a risky business that is very likely to cause periodic catastrophes. Others will believe that newer and better technologies, along with the lessons learned from those earlier disasters will make future spills unlikely. The second group is more likely to advocate drilling in the areas mentioned in this question.
Second, attitudes towards the environment are very important in making this decision. Some people believe very strongly in the need to protect the environment. They feel that oil spills do serious harm to the world and they believe that drilling for oil in general makes global warming more likely. Others think that the damage done by spills, while perhaps regrettable, is not a big deal for human beings. They may not believe that human activity causes global warming.
Finally, there are those who believe that we must have domestic sources of energy. They feel that these will increase our national security by making us less reliant on the oil from politically unstable areas such as the Middle East. This makes them feel that the benefits of drilling in our own territory are worth the risks.
Thus, answers to this question vary and there is no objective way to determine which answers are correct.