I’d assume that SoCcErTrAcK2016 said “great choices” because based on H2468L’s scores, being in state, desire to stay in the Northeast and apparent financial need, they are great choices! I would also suggest looking at Stony Brook, probably ahead of the other two even. No other SUNY schools offer BME as a major.
There are quite a few other schools with BME as a major in the region. The College Board search tool is a great way to come up with a list based on what you are looking for and your scores. If H2468L improves their test scores significantly, they might be admitted to one of the “meets full need” schools, but otherwise they would likely be gapped. I don’t consider a BS in BME a degree worth going into huge debt for from any school - the job outlook is not nearly as strong as say Electrical or Mech Eng - but that is up to the individual family.
One other thing to consider, if one is in the top 10% of their graduating HS class and pursues a STEM major, they are eligible to receive NY State’s STEM “scholarship” incentive. This is actually a loan that is forgiven if you stay in a STEM major throughout college, graduate, then work for 5 years in a STEM field in New York State after graduation. This incentive applies to SUNY/CUNY schools as well as Cornell’s statutory schools and is equivalent to the full SUNY tuition (currently $6,470 per year). Do be careful and understand what you are committing to in order to receive this, but it is another reason to stay in state.