As a US student, a step 1 score of 216 will not hold you back, except at the most competitive programs (and even there your clerkship grades and other markers of academic ability are more important). There are tons of great programs on the east coast and you would probably get interviews at most of them assuming you don't have any red flags on your application.
BU does have the option to do an MPH but for whatever reason it is one of those programs that the feeling on the interview trail is 'avoid' and they did not fill last year. The school of public health is good, but they are not as equipped as some other places at training physicians in public health. MGH/McLean and Cambridge Health Alliance in that area both have residents who are doing/have done MPHs or other degrees at Harvard during residency, and they allow you to take classes during your PGY-4 year at any of the Harvard schools. MGH has the most established global psychiatry program in the country if that's your interest. I am sure Longwood would allow you to do classes at Harvard School of Public Health (its next door) during PGY-4 but I am don't know any Longwood residents currently doing this Also unaware of specific funding for MPH at Longwood.
Mount Sinai has a global health residency track and they complete MPH coursework in global health as part of it. However, Mount Sinai does not have a school of public health and you complete your requirements in the evening. They have Craig Katz who has done lots of work in disaster psychiatry internationally, but also the response to the psychiatric consequences of 9/11 (still ongoing).
Emory has a strong MPH program, and it is possible to take classes in the schools there as a resident (presumably from PGY-3 or 4) so you could probably start working towards an MPH as a resident there. They have the strength of the CDC and some good global health work if you are interested in that. If you are interested in violence, trauma, or aspects of urban underseved populations this would be the place to go.
Duke has a global health residency track as well which includes completing an MPH (and it was possible at least to do the MPH at UNC which has a much stronger public health school than Duke).
Hopkins has arguably the best school of public health in the world (at least research and connection wise, probably less so for teaching). They have a psychiatric epidemiology fellowship, and so there are always a few who do an MPH after residency. It has probably the strongest public mental health work on the east coast. Hopkins is an acquired taste for psychiatry, and Baltimore definitely is. I do think that Hopkins is underrated for those reasons despite excellent clinical training.
If you are interested in public/health policy then George Washington is very strong on that. However I am unaware of funding to do an MPH and I would not recommend doing an MPH there. It is not the most highly regarded program, they do not have the much research, but they still manage to attract strong residents.
Columbia has an excellent MPH program, and they are strong on psychiatric epidemiology if that is your thing. I don't know if there is a formal MPH opportunity.
Yale has a global health track and a few international opportunities, but they are in their infancy in the regard. You can take classes at any of the schools from PGY-3 or PGY-4. There is no school of public health, but there is an MPH program - am not sure about funding for the MPH however.