Does he have a preference re: urban vs. suburban vs. rural?
For an honors college at a larger SUNY, Albany could be worth a look, particularly if a more urban setting would appeal. The campus is a standout in terms of racial/ethnic/economic diversity, and it has a full range of business programs. And they offer Flagship Match tuition to students from all other states: Flagship Match | University at Albany
Also in NY, Marist is a good suggestion, and nearby SUNY New Paltz is worth a look as well.
My first thought upon reading your post, though, was Miami Ohio. It’s a mid-sized public (16.5K-ish undergrads) but has always cultivated a “Public Ivy” ambience, kind of like a larger and more affordable William & Mary. (W&M itself could be worth a try as well - could be a great fit but will be a hair over budget without merit, and merit is unlikely.) With a >4.3 weighted GPA, MiamiOH would give your son at least 20K in merit as an OOS applicant, which would bring costs comfortably under your maximum; and Ohio publics guarantee the same tuition rate all four years. It may not be quite as “Northeast” as you want, but the Georgian-style campus has a Northeast vibe, and it’s not terribly hard to get to. There’s a full range of business majors, and a variety of ways to combine business and psychology. (Also an Honors College)
Would he like the idea of a co-op based program? Drexel would give him enough merit, I think, and they have a Behavioral Econ major in their business school, in addition to finance, psych, etc. etc.