3.98 is weighted or unweighted? 1420 is great for a sophomore; are you going to retake and/or give the ACT a shot?
UPenn seems to check your boxes (well, not New England but still urban northeast). https://catalog.upenn.edu/undergraduate/programs/computer-cognitive-science-bas/ It has the great financial aid you need and the kind of program you’re looking for, in a major city. But it’s probably a realistic reach only if you apply ED, as their admissions process is heavily skewed toward early decision.
With a 40K household income, are you applying for Questbridge? There are a lot of great options among the QB schools. (Some on the west coast have great CS/CogSci programs as well, like Pomona and USC).
Vassar could be a good fit academically (they have the oldest CogSci department in the country), and you’d have an application advantage since you identify as male. Might not be as urban as you want, but the access to NYC isn’t terrible. And they meet full need.
Carnegie Mellon’s CogSci major is very heavy on CS in its own right and would probably be great for what you want, and Pittsburgh is a great student city, but it’s not a full-need-met school so it’s unclear whether it would pan out financially. Same goes for RPI (plus you might not like Troy or the vibe in general).
Case Western is excellent for your interests, has a great urban college experience, and offers terrific flexibility to move among majors/programs. Perhaps not as much of a complete escape from the midwest as you’re seeking, but then again there’s a lot to like about Cleveland. U of Rochester is another with similar virtues, a little less embedded in the city that CWRU but definitely urban-adjacent. Both meet full need.
As you said, Northeastern’s CS+X programs are great. Run the NPC. They meet full need but often don’t calculate full need as generously as better-endowed schools. You can end up in a real bind if your EFC isn’t an amount you can really come up with, as any additional scholarship money you scrounge up will be taken off the bottom line of your FA offer. Tufts, on the other hand, tends to be quite generous and has great CS and CogSci programs - it’s a reach, but not necessarily out of range if you keep up the high-stats trend and strong EC’s.
Good luck; hope that helps!