I agree with a lot of other responses above. Definitely apply to Rutgers. I would be tempted to apply to both Princeton and MIT (as reaches). One additional school that you might want to consider is U.Mass Amherst.
I am not convinced that UC Merced or UC Riverside are worth both the out of state tuition and the many flights across country. I would be tempted to either apply to UC Berkeley and/or UCLA, or just stay east for your bachelor’s. Stanford might be worth an application. With regard to Stanford the quality of the university to me would justify the flights and the cost and the location is very attractive. Stanford for a master’s after getting your bachelor’s elsewhere is also a possibility (assuming that your excellent grades continue through your bachelor’s degree and that you get good internship and/or work experience).