I am hoping that you will qualify for in-state status in at least 1 of your 3 states (NY, MA or VA) because all of them have high quality public universities. I am even crossing my fingers you will qualify in more than one (as an example, my D25 has a friend who qualifies in both the state where she lives with her mom and attends high school AND in Virginia where her dad has lived for many years.) Then once I had determined in which state/s I qualified for residency, then I would apply to 2-3 public universities in each state I qualified in. I would make sure that ALL of these schools I applied to had Bio, Engineering and Math majors, unless in the next year I had 100% ruled out one of these majors.
For example, if I had residency in VA, I would apply to UVA, VTech, and 1 other (whichever one you like best of the remaining schools.) In MA, I would apply to UMass Amherst plus 2 others (Lowell, UMassBoston etc.) In NY, I would apply to Stony Brook, Bing, plus at least 1 other (Buffalo etc.)
I understand that you like Long Island, but I would not limit myself to only schools on Long Island unless for whatever reason you end up having to live with family there etc. I mean if you get into Stony Brook (and I think you will) then great. But if for some reason you don’t, I don’t think Farmington State is a suitable substitute in your case because they don’t offer most of your probable majors.