Be careful – Washington may not be as safe as you think because so many majors are impacted (including all engineering majors, CS, and biology). If you are not directly admitted as a frosh, or otherwise want to change into one of these majors, it can require a highly competitive admission process based on your college courses and grades.
http://www.washington.edu/uaa/advising/academic-planning/majors-and-minors/list-of-undergraduate-majors/
http://data.engr.washington.edu/pls/portal30/STUDENT_APPL.RPT_APPLICANT_STATISTICS_YEAR.SHOW_PARMS
Also, will your parents pay the cost of out-of-state publics and other schools like NYU that will not give you good need-based financial aid? If you are serious about medical school, you may want to consider looking for scholarships so that you can do undergraduate inexpensively and save money for expensive medical school.