Have you visited UW-Madison? It’s a vibrant setting, and far more diverse in terms of student backgrounds than you’re giving it credit for.
When you say you have a full ride vs. taking out 4K in loans at Northeastern… does this mean you have high need, and everything besides the 4K in loans will be covered by financial aid, at Northeastern? Or are you saying that you’ll be spending some unspecified amount for Northeastern, which is the maximum you can afford, and also taking out 4K in loans?
Either way, I would lean toward UW. Starting in Oakland is a disadvantage for engineering, plus many of the students at the Oakland campus don’t really want to be there, vs. Boston. The whole thing seems like a lot of logistical gymnastics in order to get to the Boston campus, and then people start leaving on co-ops as soon as sophomore spring. Overspending for this lack of continuity, when you have a full ride to a top flagship university in a great college town… I don’t see it. I’d be trying to make a visit to Madison and assuage your fears about the social aspects there.