this is going to be long, so stick with me:
Right now do you have any affordable options? If you live in NYC, did you apply to CUNY?
At my high school every single student must apply to CUNY.
If you have enough to cover the cost of attending Iona then go. You are never ever ever gonna get enough $$ to attend Penn State. Does your 50k at Iona have any loans over $5500 student loans? If there are plus loans take it off of the table.
I used to work at a school that was 85% Title I (free/reduced lunch) at that school some options were automatically off of the table; OOS universities that did not meet 100% demonstrated need. OP needs to remember that that the role of a state university system is to provide an affordable option for their taxpayer base.
The cost of the CUNY application is incorporated in the senior dues (this part is collected at the end of junior year). A parent must sign an affidavit stating that their child is opting out of CUNY and they understand that by doing so, that they may not have any financially feasible college options come spring. We document, it in ATS and all paperwork becomes part of the student permanent record (this way when a student/parent is railing that they can’t go to college and they did not get enough money, we just pull out all of our documentation).
I have straight up told Penn State, that it would be irresponsible of me to invite them to our school, because it will never be affordable to my student base (I have no one who throws long or has a great rushing game or is a Div 1 sport recruit). If a student/parent is insistent on applying, we meet, run the net price calculator together and have them fill out their affordability story as to how they are going to make this work, sign it and it becomes part of the student file because some people need to write out a plan and see in black (blue) and white how to make their situation work.
OP being a NYS resident, and having an income low enough to be Pell Eligible, should be looking first and foremost at the economic eligibility grids for opportunity programs, whether it is CD @ 2 year CUNY schools, SEEK @ 4 year CUNY Schools, EOP at most of the 64 CC & 4 year SUNY schools or HEOP at the more than 50 HEOP schools. We are talking about over 100 schools in their own back yard where they can cast a wide net to get an affordable option.
HEOP list of schools (page 10/11)
http://www.highered.nysed.gov/kiap/colldev/HEOP/documents/HEOPWebBrochure2013-14.pdf
SUNY EOP Profiles and Economic Eligibility guidelines:
http://www.suny.edu/media/suny/content-assets/documents/summary-sheets/EOP_profile.pdf
CUNY Freshman Profile (economic Guidelines will be the same, but she will know the grade/gpa ranges)
http://ithsnyc.org/2013/files/CUNYAdmission-Profile-Freshman.pdf
If OP is living and dying by engineering and is in the top 10% of her class, she is still eligible for the cost up to SUNY/CUNY tuition as at any of the SUNY/CUNY schools or the the statutory colleges at Cornell University and Alfred University, beginning in the fall term following his or her high school graduation.
https://www.hesc.ny.gov/pay-for-college/financial-aid/types-of-financial-aid/nys-grants-scholarships-awards/nys-science-technology-engineering-and-mathematics-stem-incentive-program.html
there are 36 ABET Accredited engineering programs in NYS:
http://main.abet.org/aps/accreditedprogramsearch.aspx
with the exception of the military academies, Excelsior, Iona and Pace all of them have an opportunity program attached to them (SEEK, EOP, HEOP).
If she is graduating in the top 15% of the class, she will be eligible for an NY-AIMS scholarship that she could use at any school in NYS. $500 a year for 4 years (puts a dent into the book money)
https://www.hesc.ny.gov/pay-for-college/financial-aid/types-of-financial-aid/nys-grants-scholarships-awards/nys-achievement-and-investment-in-merit-scholarship-ny-aims.html
If OP os graduating somewhere in the top 4/6 of her high school (the counselor will know how many scholarships are given at their school), she may be eligible for the NYS Scholarships for Academic Excellence provide up to $1,500 per year (for the person ranked #1 and $500 for the other recipients) for up to five years of undergraduate study in New York State.
https://www.hesc.ny.gov/pay-for-college/financial-aid/types-of-financial-aid/nys-grants-scholarships-awards/nys-scholarships-for-academic-excellence.html
My kids, know what I am going to advise them like a mantra; Follow the money. If that means, you get into Community college @CUNY with College Discovery, vs some other school that did not give you adequate aid (Iona, Pace, etc), follow the money, kill at community college, complete the associates and transfer into a EOP/HEOP program at one of the 4 year schools.
Did you apply for Questbridge? Is your school a Posse school? If yes, were you nominated and go through the process?
IF OP was hell bent on leaving NY, then she needed to look at schools where she was a viable candidate to get big merit $$ or that meets close to 100% demonstrated need.
If you do not have any affordable options, remain friends with your GC, get your recommendation letters as part of your file; regroup, take a gap year and apply again (unfortunately you will not be eligible for any of the state scholarships which you must use coming straight out of high school)
hope this helps