What college can I get in with this embarrassing SAT scores?

You do have some 4 year options within the SUNY system. My born-and-raised-in-NY nephew had about those scores and was accepted to Alfred. Others to look at are Morrisville, Oswego, Cortland, Cobleskill and Plattsburgh depending on what you want to study.

Agree, not Binghamton, too many high stats kids there.

Your choices are:
community college first, get good grades, transfer into a stronger 4-year college (even Binghamton or Baruch or CCNY or Stony Brook - after 2 years in community college, the colleges don’t look at your SAT scores anymore)
OR
go to a 4-year college that’s easier to get into