@shivng It’s not your decision to get to stay in the US after the degree. A student visa is not a work visa. You need to sponsored by an employer, and given current climate regarding immigration, that may or may not be feasible, especially with only an undergrad degree.
Who’s is going to cosign a loan for 25k a year? Do you have a parent in the US?
The most prudent approach I see is to get the undergrad in India and come here for a Master’s. The universities you have listed are all quite rigorous and love your out of state money more than they love you. Domestic students in CS and engineering programs at those places will have higher SATs and overall better prep. Lots of weeding out. Just so you are aware.