Are you a Canadian citizen or permanent resident? If so, then you have exceptionally strong (and very affordable) options in Ontario and elsewhere in Canada. Toronto, Queen’s, Waterloo, and many others are excellent universities. Graduate admissions and employers in the US know how strong these schools are.
Are you recruitable for hockey? If you are league MVP this seems likely. Harvard for example has a very good hockey team (actually two teams, men’s and woman’s). Their teams are really surprisingly strong considering that The Ivy League (which is an athletic league) does not have any sports scholarships at all. The very good Harvard hockey team must play against someone, which makes me think that other Ivy League schools such as Princeton and Yale and Cornell must also have some decent players (and I would be willing to guess that many of their players are Canadian). You might want to think about adding Cornell to your list. Northeastern and Boston University are also very good for both health sciences and hockey.
Your “strong academics strong sports” combination is what the coaches at Ivy League schools are looking for. This makes your chances difficult to predict, but probably much better than the average applicant to these schools (assuming that the coaches will care about your hockey abilities).
The same would be true about Stanford except that I do not think that they have a varsity hockey team (understandable considering California weather, but perhaps also surprising since Stanford is so strong for many other sports, and does have sports scholarships). Stanford also does not have a varsity badminton team, although they have very good badminton facilities (I played either badminton or squash very frequently when I was a student there).
MIT would be much less interested in your ability in sports. MIT is generally lousy for sports, but very strong and very demanding academically. For them your sports would be a good extracurricular activity, but not necessarily any more interesting compared to any other EC.
UVM (the University of Vermont) and the University of Massachusetts (both Amherst and Lowell campuses) have very strong hockey teams and would most likely be safeties based solely on your academics. They also have some merit scholarships, but would still cost perhaps twice what your in-province schools would cost unless you get a hockey scholarship. These are very good schools (particularly U.Mass Amherst and UVM) but I do not fully understand what advantage any of them would have over Queen’s, Toronto, Waterloo, or a long list of other Canadian universities.
You should not expect that getting a degree from a university in the US, even Harvard, Princeton, MIT, or Stanford, would allow you to stay in the US after graduating. You will be expected to return to Canada after graduation. Also, at least in my experience getting a degree from a highly ranked university in the US (at the MIT, Stanford level) will not help you at all to get a job in Canada after graduation. Employment prospects in Canada might be better with a degree from one of the very good universities in Canada.
Also, if you do decide to attend university in the USA, do not tell immigration that you intend to stay in the US after graduation. An intention to stay in the US after graduation is grounds for rejecting an application for a student visa to study in the US.