Okay, so your parents have confirmed that they are willing to pay over a quarter of a million dollars for your undergraduate degree, and you will also be able to fund an MBA (another $120K+)? It is a conversation you really want to have with your parents, as we see way too many parents who say they will cover the costs figure out in April what that really means, then decide not to pay for the places their kid has been accepted. You might want to have them run net price calculators on a few schools (even fairly high earners get aid at some schools, and just seeing the numbers is pretty important before you go too far down the road).
You really want to start by finding a couple of safeties – schools where you know you will be admitted, and you know you can afford them. But they also have to be schools you are willing to attend. Ohio State seems like an obvious choice. If your parents truly don’t care about cost, then maybe you could look at schools like Rutgers, Michigan State, Penn State, Pitt, University of Vermont, or University of Rochester. I would put a couple schools like that on your list – but you should visit, as you want to make sure a safety is a place you could see yourself attending.
Michigan (if could bring yourself to – and it is a great university) would be a low reach. Cornell is possibly a good reach – your ACT is on the low end for the Ivies overall. Northwestern is another reach to consider.
Matches - Maybe Northeastern. George Washington, mentioned above, doesn’t have a traditional campus, but is a large urban university with engineering offered It is probably a low match for you. Boston University would be another low match. Tufts would be a match, as would NYU (again, expensive, campus is not really a “campus” it the traditional sense). University of Maryland (CP) would be another match.
Note that when these colleges have schools of engineering or schools of business, you may need to apply to admission to those schools. So you either have to know what you want going in (if they take freshman admits), or rely on getting admitted partway through your time at the schools (which is a risky assumption). You have to evaluate that for each school to determine what application strategy you want to take.
This list doesn’t touch on southern schools, but there are definitely universities in the south that could work if you want to explore them as well.