i have been on an interview at Mt Sinai and i am a domestic applicant.
i don't think doing phone interviews reduces your chances. if you could go in person you would want to go in person because that way
they get a sense of you as person and a graduate student. also visiting is also good since you can meet the graduate students and ask them questions that you may have.
you can also get a feel for what the institution is like and you can also see the place that you will be spending the next 5 years of your life.
from what i can tell mount sinai is international friendly. almost 50% of their students are international, at least that is what they told us. they also have some really good faculty and it would be nice if you can meet them and see if you would like to rotate in their labs.
hope that helps.