You can apply to BU and Northeastern but you probably will end up disappointed because scholarships and financial aid at those universities do NOT stack. The scholarships will simply reduce the amount of finanical aid. Same thing for Fordham where you will just be “eligible” to get full tuition but will probably not get it.
See for example disappointing outcome at NHRP 2019 College Scholarship List - Specialty College Admissions Topics / Hispanic Students - College Confidential Forums
I would like to disclose that we live in NJ and that my NHRP son is currently studying engineering at ASU (now in his third year). We spent a lot of time a few years ago figuring out where he should apply. I have posted our story in a long thread that I think is worth reading for reference: Looking for advice in Merit aid for a top 1% student - Financial Aid & Scholarships - College Confidential Forums
In short at the time, for engineering students, ASU and University of Kentucky offered the best deals to NHRP recipients (Kentucky being better financially but ASU offering the best value imho).
University of Arizona is also great, but their scholarship was based on a combination of SAT/ACT score and GPA rather than just on being NHRP recipient (they are currently not using SAT/ACT score due to numerous high schools students not having been able to get tested because of the pandemic).
For out of state students, one advantage of ASU over University of Arizona is that PHX SkyHarbor is very close to ASU and can be reached via the Light Rail for $2. On the other hand, Univerity of Arizona has the brand new Honors Village.
I highly recommend the books “Where You Go Is Not Who You’ll Be: An Antidote to the College Admissions Mania” by Frank Bruni and “Inside Honors 2020-2021: Ratings and Reviews of 40 Public University Honors Programs” by John Willingham to help narrowing a list of colleges worth applying to.
By the way, the US News best undergraduate engineering programs rankings for 2021 are as follow:
ASU #42 Discover why the Barrett experience is right for you. | Barrett, The Honors College (asu.edu)
Northeastern #48
Boston University #53
University of Arizona #53 Honors Village | Honors College (arizona.edu)
University of Kentucky #90 Home | Honors College (uky.edu)