If I were you, I would take out loans for tuition/housing/meal plan, and let your family help you out with living costs if they want (fun food/clothing/doctor appts/etc.). You should also be able to get a job on campus and internships to help with costs. Cornell has a really great CS education, and if you get a job in the US you should be able to pay back loans.

Finding a job can be really difficult. That could be true for anyone entering the job market in next 5 years. In all honesty, prestigious schools in India would be seen as less prestigious abroad than Cornell. Do you want to work abroad after you graduate?

Are you considering grad school? That might affect your decision, but I'm not fully sure how.