trade school wouldn’t count - colleges that take “first gen” into account mean “no 4-year degree”.
NYS has good public universities, each with areas where they especially shine; you can start exploring them through virtual tours or when you go visit places around the state.
Binghamton and Geneseo are more residential, Stony Brook is more “suitcase”/commuter.
(Not sure whether this will be redundant with what you know but just in case:
Residential universities tend to provide more support and more activities on campus, often at no or low cost, to their students than “suitcase”/commuter universities where the students go home at night. However commuting can lower university costs.
The US also has a unique system of Liberal Arts Colleges, where the focus is on undergraduate students through close interactions with faculty.)
Cornell university has “contract” colleges where NYS residents have a special rate.
40K/year is a good budget that will open many possibilities beside SUNYs.
Run the NPC on Connecticut College, Marist, Dickinson for instance. What do these colleges think you can afford and does it match what you think you can afford?