The competitiveness of MIT for international students cannot be understated. It is ridiculously competitive even for US applicants - many students with perfect stats and impressive extracurriculars are denied. Because of the combination of reputation, and being one of a tiny handful of US schools that are need-blind and meet full need for internationals… and add to that the fact that they limit international enrollment to 10% of undergraduates… this is the longest of long shots.
Penn and Columbia are need-aware for non-US applicants, so your chances are better if you do not apply for financial aid than if you do. (If you do apply for aid and still get in, they will meet full documented need.) They admit more internationals than MIT does, but it’s still a very steep admission path. NYU is a little less steep because its budget depends on large numbers of full-pay international students. Even if you apply for aid, NYU won’t meet full need, not even for US students much less international ones.   Northeastern is in the same category - they love their full-pay international students (although unlike NYU they do meet full need for their US students, made possible in part by international dollars).  The question there is, do you even want to be one of the students who full-pays over $300K to pad the bottom line of one of these schools?
The public U’s you are looking at would be a better financial deal, and the UI and UT business schools are comparable in reputation to the private ones. It’s still going to be very tough to be admitted unless you can raise your test scores, and not a sure bet even with a near-perfect SAT.  Davis and Drexel are realistic, I think, but Drexel will be $$$ and Davis, as Gumbymom says, doesn’t have an undergrad finance major - and your price for a UC would be as high as some private U’s - around $65K/year.
In terms of private U’s that could possibly be worth full price, you might want to consider Lehigh, which is especially known for finance - this is its most popular major.  For a co-op program that’s comparable to Drexel’s and Northeastern’s at a public U price, look at U of Cincinnati http://catalog.sou.edu/content.php?catoid=2&navoid=131
Other public U’s to consider:
[Berkeley, UMichigan, UVA, UCLA, UW-Seattle, UNC, Georgia Tech - assume you may already have ruled these out based on competitiveness and cost?]
But Arizona State, UMinn-Twin Cities, Penn State, Ohio State, Michigan State, UGA, UW-Madison, UT-Dallas, Rutgers, UTenn-Knoxville, U of Utah, UIUC, UMD, Pitt, Purdue, William & Mary, and UMass Amherst… ALL of these have higher-ranked business programs than Northeastern. The Missouri, Alabama, Arkansas, Colorado, South Carolina, Arizona, Kansas, and Oklahoma flagship U’s, as well as SUNY’s Buffalo & Binghamton, Auburn, and Iowa State, all outrank Drexel. (Not to overemphasize rankings, and this is at the MBA level, but just to make the point that there are many excellent b-schools at relatively-affordable public universities all over the US.)
William and Mary might be a particularly good one to look at, as it has a “public ivy” reputation and it’s making a specific effort to recruit international students right now. (It’s more expensive than many publics, but still under $60K/year.)
Given that you don’t sound as if full-paying for a private U would be easy for your family, and that your qualifications fall more into what people on CC call the “average excellent” range rather than the super-high-stats + national/international-level awards & distinctions range that it takes to get into the super-elites…  I would really encourage you to give public U’s a closer look and re-balance your list to emphasize schools that you can both get into and realistically afford. The schools you are targeting would be tough admits for a US student with your credentials, and for the most part being an international student makes it that much tougher. You sound like an excellent student, and many excellent schools will be happy to accept you, but you need more true matches and safeties to avoid being disappointed and/or having to over-pay for a private U that isn’t measurably better than the more affordable public alternatives.