At least in our experience internships and coops are great for the work experience, but are not something that actually helps in a significant way with the cost of education. I would not count on the coop program reducing the overall cost.
Both daughters had internships or a coop over various summers, and the pay did mostly exceed the cost of living but not by all that much. Both were already at affordable universities so we mostly were just glad for them to get the experience, which was very valuable in both cases.
Also, of course internships and coops are available at a wide range of universities (not just Northeastern), and engineering is not a major that makes it easy (or even feasible) to graduate early. I have heard of a few cases of students taking one or two extra semesters to graduate with a degree in engineering. For math in graduate school for a master’s degree I did know a few students who took one extra quarter over the summer to complete their degree (I got my master’s degree in a sub-field of applied math at a university that is on the quarter system). I was slightly jealous since stretching things out for an extra quarter did allow them to take a lighter course load, but my budget did not allow this at the time.
When we were budgeting for university, we did set a budget that would not have been a major problem if either daughter had taken an extra year before graduating.
And there are a lot of universities that are very good for engineering and for computer science, and for mathematics. I would pick a school that is clearly going to be affordable. I do not think that this describes Northeastern in your case.