You could probably accomplish most of the goals you mentioned in your email if you work hard and with passion in any field, even outside engineering. Regarding money, I always tell my students that if you work hard, with passion in a field you really like, then money will come. Employers will see you as a reliable worker and a doer and the raises and promotions will naturally appear. However, if living in NYC and having a very high salary is a priority, as well as working in a building and going to Harvard, perhaps being a banker is more what you have in mind. You need to consider those feelings and how strong they are. AN engineer makes around $45K after graduation but it could be more. An engineer with a masters degree anywhere between $60K and $100. But there are many CEOs that are engineers, so what i am gving you is simply a ballpark estimate. Many engineers have their own companies and make lots of money as well. But if dealing with businesses and making money is something that you think is moving you more than anything else, you might want to explore other careers such as business or finance first. But do not discard engineering. THere are several new specialties these days that might suit you just as well. Industrial engineering for example is dealing more and more with services than with manufacturing. There is a new area of IE called financial engineering that deals with designing decision support systems for banks and financial institutions. While FE is a graduate degree, it is within engineering.
However, to be an engineer you need to like math and science, and like to design or plan for new things, at least a little. Whether a bridge or a new robot, or a new information system for a bank, engineers are always designing or planning. You also need to have lots of discipline and acquire good study habits.
You do not mention your age but maybe you still have time to decide. I would visit an engineering school of your choice and ask questions to the professors and students and ask them to let you sit in one freshmen class and one senior class for you to have a taste of what the career is about and the effort involved in getting the diploma. But before, browse the web for the different engineering fields, visit the professional associations of each specialty, and browse the jobs. Then narrow it down to 2 fields that attract you and visit a school with offerings in such areas.
I hope I helped you some and I wish you luck in your search.