If your income is 45k or so, you’re eligible for fee waivers. Ask your HS college counselor.
If you mean rhe cost of college rather thn cost of application, you really need to run the NPC on 1 each of: SUNYs, LAC, Private U.
Is your HS a selective/exam based school?
Apply to Questbridge and rank a mix of universities and LACs (all colleges on the Questbridge list are super prestigious, even if you’ve not heard of them trust that they know their peers.)
If your parents want Ivies on your list, Brown is not a bad idea - you don’t really stand a chance imho but they’re looking for more FGLI applicants so if your HS is competitive and adcoms know a 90% there indicates a strong performance, well, odds may be 5%.
Cornell would be the other one: review the majors offered in CALS carefully and apply to one of them. As a NY resident you’d have some priority. Still a high reach but worth a try.
Why Bucknell? It’s very different from the others, very Greek.
Drop Syracuse: they don’t meet need.
Look into Dickinson, Lafayette, Franklin&Marshall, Muhlenberg, Skidmore, St Lawrence.
SUNYs : Binghamton, Geneseo, Stony Brook, Buffalo all make sense and should be on your list. Add a few others as safeties: New Paltz, Oneonta, Fredonia? Apply to Honors whenever available.
Seconding Macaulay and Sophie Davis programs.